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## Golubitsky, Martin A.

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 Author ID: golubitsky.martin-a Published as: Golubitsky, M.; Golubitsky, Martin; Golubitsky, Martin A.; Golubitsky, Marty Homepage: http://people.mbi.ohio-state.edu/golubitsky.4/ External Links: MGP · Wikidata · ORCID · dblp · GND
 Documents Indexed: 166 Publications since 1971, including 18 Books Biographic References: 1 Publication
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#### Co-Authors

 5 single-authored 39 Stewart, Ian Nicholas 15 Schaeffer, David G. 9 Dellnitz, Michael 8 Wang, Yunjiao 7 Field, Michael J. 5 Antoneli, Fernando jun. 5 Chossat, Pascal 5 Dias, Ana Paula S. 5 Dionne, Benoit 5 Keyfitz, Barbara Lee 5 Melbourne, Ian 5 Nicol, Matthew 4 Buono, Pietro-Luciano 4 Guillemin, Victor W. 4 Knobloch, Edgar 4 Krupa, Martin 4 Langford, William F. 4 Marsden, Jerrold Eldon 4 Shiau, LieJune 4 Tischler, David C. 3 Diekman, Casey O. 3 Josić, Krešimir 3 Török, Andrei 3 Wang, Yangyang 2 Aguiar, Manuela A. D. 2 Aronson, Donald G. 2 Barany, Ernest 2 Best, Janet A. 2 Bressloff, Paul C. 2 Broer, Henk W. 2 Buzano, Ernesto 2 Chillingworth, David R. 2 Cowan, Jack D. 2 Crawford, John David 2 Da Conceição A. Leite, Maria 2 Duncan, William 2 Gillis, David B. 2 Hohmann, Andreas 2 LeBlanc, Victor G. 2 Nijhout, H. Frederik 2 Nordstrøm Jensen, Carsten 2 Palacios, Antonio 2 Pivato, Marcus 2 Postlethwaite, Claire M. 2 Reed, Michael C. 2 Romano, David Gilman 2 Rothschild, Bruce L. 2 Thomas, Peter J. 2 True, Hans 2 van Gils, Stephan A. 2 Vegter, Gert 1 Allgower, Eugene L. 1 Alves-Pinto, Carla 1 Bloch, Anthony M. 1 Böhmer, Klaus 1 Cendra, Hernán 1 Chadam, John M. 1 Chorin, Alexandre Joel 1 Collins, James J. 1 Comanici, Adela N. 1 Desbrun, Mathieu 1 Elmhirst, Toby 1 Epstein, Irving R. 1 Farr, William W. 1 Field, Mike J. 1 Filipski, Natasha 1 Gandhi, Punit 1 Gomes, M. Gabriela M. 1 Gotay, Mark J. 1 Guckenheimer, John M. 1 Hao, Wenrui 1 Hou, Chuanze 1 Huang, Zhengyuan 1 Ihrig, Edwin C. 1 Iooss, Gérard 1 Isenberg, Jim 1 Kaper, Tasso J. 1 Keeler, Emmett B. 1 Krishnaprasad, P.s. 1 Lam, King-Yeung 1 Lauterbach, Reiner 1 Leite, Maria Conceição A. 1 Li, Kaitai 1 Lim, Chjan C. 1 Lou, Yuan 1 Luss, Dan 1 Ma, Jun 1 Mallet-Paret, John Joseph 1 Mao, Jianmin 1 Marsden, Alison L. 1 McMillen, Tyler 1 Messi, Leopold Matamba 1 Montgomery, Richard 1 Ortiz, Michael 1 Pinto, Carla M. A. 1 Ratiu, Tudor Stefan 1 Raugel, Geneviève 1 Roberts, Richard Mark 1 Rothschild, Michael 1 Scheurle, Jürgen ...and 16 more Co-Authors
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#### Serials

 13 Physica D 12 Nonlinearity 12 SIAM Journal on Applied Dynamical Systems 6 Journal of Nonlinear Science 5 Journal of Mathematical Biology 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 SIAM Journal on Mathematical Analysis 3 Archive for Rational Mechanics and Analysis 3 Communications on Pure and Applied Mathematics 3 Journal of Differential Equations 3 SIAM Journal on Applied Mathematics 3 Dynamical Systems 2 Communications in Mathematical Physics 2 Bulletin of Mathematical Biology 2 Advances in Mathematics 2 Proceedings of the American Mathematical Society 2 Dynamics and Stability of Systems 2 Bulletin of the American Mathematical Society. New Series 2 Notices of the American Mathematical Society 2 Discrete and Continuous Dynamical Systems 2 Chaos 2 Applied Mathematical Sciences 2 Graduate Texts in Mathematics 2 The Journal of Mathematical Neuroscience 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Mathematical Biosciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Inventiones Mathematicae 1 Journal of Differential Geometry 1 Pacific Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Ser. A 1 Theoretical Population Biology 1 Transactions of the American Mathematical Society 1 Delft Progress Report 1 Neural Computation 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Review 1 Journal of Dynamics and Differential Equations 1 Philosophical Transactions of the Royal Society of London. Series A 1 Tatra Mountains Mathematical Publications 1 Bulletin of the American Mathematical Society 1 Contemporary Mathematics 1 Fields Institute Communications 1 The IMA Volumes in Mathematics and its Applications 1 ISNM. International Series of Numerical Mathematics 1 Progress in Mathematics 1 São Paulo Journal of Mathematical Sciences 1 Dynamic Games and Applications 1 Journal of Theoretical Biology
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#### Fields

 92 Dynamical systems and ergodic theory (37-XX) 68 Ordinary differential equations (34-XX) 42 Global analysis, analysis on manifolds (58-XX) 36 Biology and other natural sciences (92-XX) 23 Partial differential equations (35-XX) 15 Fluid mechanics (76-XX) 11 Manifolds and cell complexes (57-XX) 9 General and overarching topics; collections (00-XX) 6 Topological groups, Lie groups (22-XX) 6 Mechanics of particles and systems (70-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Group theory and generalizations (20-XX) 5 Numerical analysis (65-XX) 4 Mechanics of deformable solids (74-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Nonassociative rings and algebras (17-XX) 2 Combinatorics (05-XX) 2 Operator theory (47-XX) 2 Differential geometry (53-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH

146 Publications have been cited 4,013 times in 2,396 Documents Cited by Year
Stable mappings and their singularities. Zbl 0294.58004
Golubitsky, M.; Guillemin, V.
1973
Singularities and groups in bifurcation theory. Volume II. Zbl 0691.58003
Golubitsky, Martin; Stewart, Ian; Schaeffer, David G.
1988
Singularities and groups in bifurcation theory. Volume I. Zbl 0607.35004
Golubitsky, Martin; Schaeffer, David G.
1985
The symmetry perspective. From equilibrium to chaos in phase space and physical space. Zbl 1031.37001
Golubitsky, Martin; Stewart, Ian
2002
A theory for imperfect bifurcation via singularity theory. Zbl 0409.58007
Golubitsky, M.; Schaeffer, D.
1979
Nonlinear dynamics of networks: the groupoid formalism. Zbl 1119.37036
Golubitsky, Martin; Stewart, Ian
2006
Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032
Stewart, Ian; Golubitsky, Martin; Pivato, Marcus
2003
Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030
Golubitsky, Martin; Stewart, Ian; Török, Andrei
2005
Hopf bifurcation in the presence of symmetry. Zbl 0588.34030
Golubitsky, Martin; Stewart, Ian
1985
Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford. Zbl 0956.00057
Golubitsky, M. (ed.); Knobloch, E. (ed.)
2000
Classification and unfoldings of degenerate Hopf bifurcations. Zbl 0442.58020
Golubitsky, Martin; Langford, William F.
1981
Imperfect bifurcation in the presence of symmetry. Zbl 0467.58019
Golubitsky, M.; Schaeffer, D.
1979
Symmetries and pattern selection in Rayleigh-Bénard convection. Zbl 0599.76098
Golubitsky, M.; Swift, J. W.; Knobloch, E.
1984
Symmetry-increasing bifurcation of chaotic attractors. Zbl 0668.58038
Chossat, P.; Golubitsky, M.
1988
A modular network for legged locomotion. Zbl 1039.92009
Golubitsky, Martin; Stewart, Ian; Buono, Pietro-Luciano; Collins, J. J.
1998
Symmetry in chaos. A search for pattern in mathematics, art and nature. Zbl 0765.58001
Field, Michael; Golubitsky, Martin
1992
Pattern selection with $$\mathrm{O}(3)$$ symmetry. Zbl 0581.22021
Ihrig, E.; Golubitsky, M.
1984
Bifurcation on the hexagonal lattice and the planar Bénard problem. Zbl 0622.76052
Buzano, E.; Golubitsky, M.
1983
Heteroclinic cycles involving periodic solutions in mode interactions with $$O(2)$$ symmetry. Zbl 0737.58042
Melbourne, I.; Chossat, P.; Golubitsky, M.
1989
Boundary conditions and mode jumping in the buckling of a rectangular plate. Zbl 0414.73036
Schaeffer, David; Golubitsky, Martin
1979
Models of central pattern generators for quadruped locomotion. I: Primary gaits. Zbl 1039.92007
Buono, Pietro-Luciano; Golubitsky, Martin
2001
Symmetry and stability in Taylor-Couette flow. Zbl 0603.76053
Golubitsky, Martin; Stewart, Ian
1986
Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators. Zbl 0602.58038
Golubitsky, Martin; Stewart, Ian
1986
Coupled cells with internal symmetry. I: Wreath products. Zbl 0894.58049
Dionne, Benoit; Golubitsky, Martin; Stewart, Ian
1996
Convergence of the age structure: applications of the projective metric. Zbl 0297.92014
Golubitsky, Martin; Keeler, Emmett B.; Rothschild, Michael
1975
Some curious phenomena in coupled cell networks. Zbl 1136.37359
Golubitsky, M.; Nicol, M.; Stewart, I.
2004
Bifurcation problems with hidden symmetries. Zbl 0567.58004
Golubitsky, M.; Marsden, J.; Schaeffer, D.
1984
Bifurcations from regular quotient networks: A first insight. Zbl 1155.37315
Aguiar, Manuela A. D.; Dias, Ana Paula S.; Golubitsky, Martin; Da Conceição A. Leite, Maria
2009
Bifurcation analysis near a double eigenvalue of a model chemical reaction. Zbl 0522.35010
Schaeffer, David G.; Golubitsky, Martin A.
1981
Homogeneous three-cell networks. Zbl 1114.34035
Leite, Maria da Conceição A.; Golubitsky, Martin
2006
Coupled arrays of Josephson junctions and bifurcation of maps with $$S_ N$$ symmetry. Zbl 0803.58040
Aronson, D. G.; Golubitsky, Martin; Krupa, Martin
1991
The structure of symmetric attractors. Zbl 0805.58043
Melbourne, Ian; Dellnitz, Michael; Golubitsky, Martin
1993
Ponies on a merry-go-round in large arrays of Josephson junctions. Zbl 0732.58031
Aronson, D. G.; Golubitsky, Martin; Mallet-Paret, John
1991
Iterates of maps with symmetry. Zbl 0694.58030
Chossat, Pascal; Golubitsky, Martin
1988
Generic bifurcation of Hamiltonian systems with symmetry. With an appendix by Jerrold Marsden. Zbl 0612.58013
Golubitsky, Martin; Stewart, Ian
1987
Coupled cells with internal symmetry. II: Direct products. Zbl 0894.58050
Dionne, Benoit; Golubitsky, Martin; Stewart, Ian
1996
Planforms in two and three dimensions. Zbl 0774.35055
Dionne, Benoit; Golubitsky, Martin
1992
What geometric visual hallucinations tell us about the visual cortex. Zbl 1037.91083
Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.; Wiener, Matthew C.
2002
Boundary conditions as symmetry constraints. Zbl 0735.35007
Crawford, J. D.; Golubitsky, M.; Gomes, M. G. M.; Knobloch, E.; Stewart, I. N.
1991
Bifurcations with O(3) symmetry including applications to the Benard problem. Zbl 0492.58012
Golubitsky, Martin; Schaeffer, David
1982
A classification of degenerate Hopf bifurcations with O(2) symmetry. Zbl 0635.34036
Golubitsky, Martin; Roberts, Mark
1987
Central pattern generators for bipedal locomotion. Zbl 1100.92011
Pinto, Carla M. A.; Golubitsky, Martin
2006
Two-color patterns of synchrony in lattice dynamical systems. Zbl 1066.34049
Wang, Yunjiao; Golubitsky, Martin
2005
The constrained Liapunov-Schmidt procedure and periodic orbits. Zbl 0833.58014
Golubitsky, Martin; Marsden, Jerrold E.; Stewart, Ian; Dellnitz, Michael
1995
Bifurcations from synchrony in homogeneous networks: linear theory. Zbl 1165.37018
Golubitsky, Martin; Lauterbach, Reiner
2009
Time-reversibility and particle sedimentation. Zbl 0717.58049
Golubitsky, Martin; Krupa, Martin; Lim, Chjan
1991
Nilpotent Hopf bifurcations in coupled cell systems. Zbl 1141.34324
Elmhirst, Toby; Golubitsky, Martin
2006
Heteroclinic cycles in rings of coupled cells. Zbl 1011.34035
Buono, Pietro-Luciano; Golubitsky, Martin; Palacios, Antonio
2000
Cycling chaos. Zbl 0886.58077
Dellnitz, Michael; Field, Michael; Golubitsky, Martin; Ma, Jun; Hohmann, Andreas
1995
Detecting the symmetry of attractors. Zbl 0783.58042
Barany, Ernest; Dellnitz, Michael; Golubitsky, Martin
1993
Contact equivalence for Lagrangian manifolds. Zbl 0295.57018
Golubitsky, M.; Guillemin, V.
1975
Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex. Zbl 1017.37025
Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.
2001
Hopf bifurcation from rotating waves and patterns in physical space. Zbl 0988.76036
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
2000
Fearful symmetry: is God a geometer? Zbl 0931.00014
Stewart, Ian; Golubitsky, Martin
1992
Pattern formation and bistability in flow between counterrotating cylinders. Zbl 0656.76088
Golubitsky, M.; Langford, W. F.
1988
Interior symmetry and local bifurcation in coupled cell networks. Zbl 1067.37066
Golubitsky, M.; Pivato, M.; Stewart, I.
2004
The geometry of resonance tongues: a singularity theory approach. Zbl 1035.37035
Broer, Henk W.; Golubitsky, Martin; Vegter, Gert
2003
Meandering of the spiral tip: an alternative approach. Zbl 0902.58025
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
1997
Symmetry of attractors and the Karhunen-Loève decomposition. Zbl 0806.76087
Dellnitz, Michael; Golubitsky, Martin; Nicol, Matthew
1994
An introduction to catastrophe theory and its applications. Zbl 0389.58007
Golubitsky, Martin
1978
Homeostasis, singularities, and networks. Zbl 1369.92040
Golubitsky, Martin; Stewart, Ian
2017
Patterns of synchrony in lattice dynamical systems. Zbl 1079.37061
Antoneli, Fernando; Dias, Ana Paula S.; Golubitsky, Martin; Wang, Yunjiao
2005
An unfolding theory approach to bursting in fast-slow systems. Zbl 1215.34043
Golubitsky, Martin; Josić, Krešimir; Kaper, Tasso J.
2001
Feed-forward networks, center manifolds, and forcing. Zbl 1257.34025
Golubitsky, Martin; Postlethwaite, Claire
2012
Target patterns and spirals in planar reaction-diffusion systems. Zbl 0965.35084
Golubitsky, M.; Knobloch, E.; Stewart, I.
2000
The Morse lemma in infinite dimensions via singularity theory. Zbl 0525.58013
Golubitsky, Martin; Marsden, Jerrold
1983
Synchrony-breaking bifurcation at a simple real eigenvalue for regular networks 1:1-dimensional cells. Zbl 1235.37011
Stewart, Ian; Golubitsky, Martin
2011
Winding numbers and average frequencies in phase oscillator networks. Zbl 1130.37345
Golubitsky, M.; Josic, K.; Shea-Brown, E.
2006
A qualitative study of the steady-state solutions for a continuous flow stirred tank chemical reactor. Zbl 0448.58001
Golubitsky, M.; Keyfitz, B. L.
1980
Stable mappings and their singularities. 2nd corr. printing. Zbl 0434.58001
Golubitsky, M.; Guillemin, V.
1980
Stable mappings and their singularities. (Ustojchivye otobrazheniya i ikh osobennosti.) Transl. from the English by A. G. Kushnirenko. Ed. by V. I. Arnol’d. Zbl 0429.58004
Golubitsky, M.; Guillemin, V.
1977
Primitive actions and maximal subgroups of Lie groups. Zbl 0265.22024
Golubitsky, Martin
1972
Network periodic solutions: full oscillation and rigid synchrony. Zbl 1216.34029
Golubitsky, Martin; Romano, David; Wang, Yunjiao
2010
Stability computations for nilpotent Hopf bifurcations in coupled cell systems. Zbl 1141.37343
Golubitsky, M.; Krupa, M.
2007
Spatiotemporal symmetries in the disynaptic canal-neck projection. Zbl 1129.92015
Golubitsky, Martin; Shiau, Liejune; Stewart, Ian
2007
An example of symmetry breaking to heteroclinic cycles. Zbl 0991.34043
Hou, Chuanze; Golubitsky, Martin
1997
Symmetric patterns in linear arrays of coupled cells. Zbl 1055.80505
Epstein, Irving R.; Golubitsky, Martin
1993
Bifurcations on hemispheres. Zbl 0791.35044
Field, M.; Golubitsky, M.; Stewart, I.
1991
Hopf-Hopf mode interactions with O(2) symmetry. Zbl 0656.34020
Chossat, Pascal; Golubitsky, Martin; Keyfitz, Barbara Lee
1986
Multiparameter bifurcation theory. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 14-20, 1985, with support from the National Science Foundation (at Humboldt State University, Arcata, California). Zbl 0587.00009
Golubitsky, Martin (ed.); Guckenheimer, John M. (ed.)
1986
A singularity theory analysis of a thermal-chainbranching model for the explosion peninsula. Zbl 0497.58006
Golubitsky, Martin; Keyfitz, Barbara Lee; Schaeffer, David G.
1981
Analysis of homeostatic mechanisms in biochemical networks. Zbl 1382.92131
Reed, Michael; Best, Janet; Golubitsky, Martin; Stewart, Ian; Nijhout, H. Frederik
2017
Derived patterns in binocular rivalry networks. Zbl 1291.92032
Diekman, Casey O.; Golubitsky, Martin; Wang, Yunjiao
2013
Bifurcation on the visual cortex with weakly anisotropic lateral coupling. Zbl 1088.37508
Golubitsky, Martin; Shiau, Lie June; Török, Andrei
2003
Patterns in square arrays of coupled cells. Zbl 0889.34033
Gillis, David; Golubitsky, Martin
1997
Modulated rotating waves in O(2) mode interactions. Zbl 0681.58029
Crawford, John David; Golubitsky, Martin; Langford, William F.
1988
A discussion of symmetry and symmetry breaking. Zbl 0535.58010
Golubitsky, Martin; Schaeffer, David
1983
Reduction and dynamics of a generalized rivalry network with two learned patterns. Zbl 1263.37068
Diekman, Casey; Golubitsky, Martin; McMillen, Tyler; Wang, Yunjiao
2012
Network periodic solutions: patterns of phase-shift synchrony. Zbl 1245.34043
Golubitsky, Martin; Romano, David; Wang, Yunjiao
2012
Symmetry in chaos: a search for pattern in mathematics, art and nature. 2nd ed. Zbl 1173.37001
Field, Michael; Golubitsky, Martin
2009
Patterns of oscillation in coupled cell systems. Zbl 1017.37045
Golubitsky, Martin; Stewart, Ian
2002
Symmetry detectives for SBR attractors. Zbl 0838.34055
Golubitsky, Martin; Nicol, Matthew
1995
Coupled cells: Wreath products and direct products. Zbl 0810.34028
Golubitsky, Martin; Stewart, Ian; Dionne, Benoit
1994
Mechanisms of symmetry creation. Zbl 0803.35011
Dellnitz, Michael; Golubitsky, Martin; Melbourne, Ian
1992
Primitive subalgebras of exceptional Lie algebras. Zbl 0209.06602
Golubitsky, M.; Rothschild, B.
1971
Homeostasis in a feed forward loop gene regulatory motif. Zbl 1397.92179
Antoneli, Fernando; Golubitsky, Martin; Stewart, Ian
2018
Network symmetry and binocular rivalry experiments. Zbl 1321.92044
Diekman, Casey O.; Golubitsky, Martin
2014
Synchrony versus symmetry in coupled cells. Zbl 1112.34020
Golubitsky, Martin; Stewart, Ian
2005
Symmetry and pattern formation in coupled cell networks. Zbl 0987.37041
Golubitsky, Martin; Stewart, Ian
1999
Spirals in scalar reaction-diffusion equations. Zbl 0886.58102
Dellnitz, Michael; Golubitsky, Martin; Hohmann, Andreas; Stewart, Ian
1995
Infinitesimal homeostasis in three-node input-output networks. Zbl 1436.92009
Golubitsky, Martin; Wang, Yangyang
2020
Homeostasis in a feed forward loop gene regulatory motif. Zbl 1397.92179
Antoneli, Fernando; Golubitsky, Martin; Stewart, Ian
2018
Homeostasis with multiple inputs. Zbl 1395.92067
Golubitsky, Martin; Stewart, Ian
2018
Homeostasis despite instability. Zbl 1392.92024
Duncan, W.; Best, J.; Golubitsky, M.; Nijhout, H. F.; Reed, M.
2018
Homeostasis, singularities, and networks. Zbl 1369.92040
Golubitsky, Martin; Stewart, Ian
2017
Analysis of homeostatic mechanisms in biochemical networks. Zbl 1382.92131
Reed, Michael; Best, Janet; Golubitsky, Martin; Stewart, Ian; Nijhout, H. Frederik
2017
Coordinate changes for network dynamics. Zbl 1362.37051
Golubitsky, Martin; Stewart, Ian
2017
Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics. Zbl 1382.92023
Golubitsky, Martin; Stewart, Ian
2016
Singularity theory of fitness functions under dimorphism equivalence. Zbl 1352.58008
Wang, Xiaohui; Golubitsky, Martin
2016
Symmetry types and phase-shift synchrony in networks. Zbl 1364.34045
Golubitsky, Martin; Messi, Leopold Matamba; Spardy, Lucy E.
2016
Normal forms and unfoldings of singular strategy functions. Zbl 1348.91047
Vutha, Amit; Golubitsky, Martin
2015
Bifurcations in forced response curves. Zbl 1331.34069
Wiser, Justin; Golubitsky, Martin
2015
Symmetry methods in mathematical biology. Zbl 1346.92011
Golubitsky, Martin; Stewart, Ian
2015
Network symmetry and binocular rivalry experiments. Zbl 1321.92044
Diekman, Casey O.; Golubitsky, Martin
2014
Derived patterns in binocular rivalry networks. Zbl 1291.92032
Diekman, Casey O.; Golubitsky, Martin; Wang, Yunjiao
2013
Feed-forward networks, center manifolds, and forcing. Zbl 1257.34025
Golubitsky, Martin; Postlethwaite, Claire
2012
Reduction and dynamics of a generalized rivalry network with two learned patterns. Zbl 1263.37068
Diekman, Casey; Golubitsky, Martin; McMillen, Tyler; Wang, Yunjiao
2012
Network periodic solutions: patterns of phase-shift synchrony. Zbl 1245.34043
Golubitsky, Martin; Romano, David; Wang, Yunjiao
2012
Synchrony-breaking bifurcation at a simple real eigenvalue for regular networks 1:1-dimensional cells. Zbl 1235.37011
Stewart, Ian; Golubitsky, Martin
2011
Periodically forced Hopf bifurcation. Zbl 1247.34059
Zhang, Yanyan; Golubitsky, Martin
2011
Network periodic solutions: full oscillation and rigid synchrony. Zbl 1216.34029
Golubitsky, Martin; Romano, David; Wang, Yunjiao
2010
The abelian Hopf $$H$$ mod $$K$$ theorem. Zbl 1198.37088
Filipski, Natasha; Golubitsky, Martin
2010
Bifurcations from regular quotient networks: A first insight. Zbl 1155.37315
Aguiar, Manuela A. D.; Dias, Ana Paula S.; Golubitsky, Martin; Da Conceição A. Leite, Maria
2009
Bifurcations from synchrony in homogeneous networks: linear theory. Zbl 1165.37018
Golubitsky, Martin; Lauterbach, Reiner
2009
Symmetry in chaos: a search for pattern in mathematics, art and nature. 2nd ed. Zbl 1173.37001
Field, Michael; Golubitsky, Martin
2009
Patterns on growing square domains via mode interactions. Zbl 1151.65069
2008
Stability computations for nilpotent Hopf bifurcations in coupled cell systems. Zbl 1141.37343
Golubitsky, M.; Krupa, M.
2007
Spatiotemporal symmetries in the disynaptic canal-neck projection. Zbl 1129.92015
Golubitsky, Martin; Shiau, Liejune; Stewart, Ian
2007
Homogeneous coupled cell networks with $$S_3$$-symmetric quotient. Zbl 1163.34305
Aguiar, M. A. D.; Dias, A. P. S.; Golubitsky, M.; Leite, M. C. A.
2007
Geometry of resonance tongues. Zbl 1120.37034
Broer, Henk W.; Golubitsky, Martin; Vegter, Gert
2007
Synchrony in lattice differential equations. Zbl 1179.37106
Antonelli, Fernando; Dias, Ana Paula S.; Golubitsky, Martin; Wang, Yunjiao
2007
Nonlinear dynamics of networks: the groupoid formalism. Zbl 1119.37036
Golubitsky, Martin; Stewart, Ian
2006
Homogeneous three-cell networks. Zbl 1114.34035
Leite, Maria da Conceição A.; Golubitsky, Martin
2006
Central pattern generators for bipedal locomotion. Zbl 1100.92011
Pinto, Carla M. A.; Golubitsky, Martin
2006
Nilpotent Hopf bifurcations in coupled cell systems. Zbl 1141.34324
Elmhirst, Toby; Golubitsky, Martin
2006
Winding numbers and average frequencies in phase oscillator networks. Zbl 1130.37345
Golubitsky, M.; Josic, K.; Shea-Brown, E.
2006
Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030
Golubitsky, Martin; Stewart, Ian; Török, Andrei
2005
Two-color patterns of synchrony in lattice dynamical systems. Zbl 1066.34049
Wang, Yunjiao; Golubitsky, Martin
2005
Patterns of synchrony in lattice dynamical systems. Zbl 1079.37061
Antoneli, Fernando; Dias, Ana Paula S.; Golubitsky, Martin; Wang, Yunjiao
2005
Synchrony versus symmetry in coupled cells. Zbl 1112.34020
Golubitsky, Martin; Stewart, Ian
2005
Bursting in coupled cell systmes. Zbl 1404.92052
Golubitsky, Martin; Josić, Krešimir; Shiau, Liejune
2005
Bipedal locomotion. Zbl 1099.92005
Golubitsky, Martin; Alves-Pinto, Carla
2005
Some curious phenomena in coupled cell networks. Zbl 1136.37359
Golubitsky, M.; Nicol, M.; Stewart, I.
2004
Interior symmetry and local bifurcation in coupled cell networks. Zbl 1067.37066
Golubitsky, M.; Pivato, M.; Stewart, I.
2004
Symmetry and pattern formation on the visual cortex. Zbl 1079.92011
Golubitsky, Martin; Shiau, LieJune; Török, Andrei
2004
Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032
Stewart, Ian; Golubitsky, Martin; Pivato, Marcus
2003
The geometry of resonance tongues: a singularity theory approach. Zbl 1035.37035
Broer, Henk W.; Golubitsky, Martin; Vegter, Gert
2003
Bifurcation on the visual cortex with weakly anisotropic lateral coupling. Zbl 1088.37508
Golubitsky, Martin; Shiau, Lie June; Török, Andrei
2003
Bifurcation and planar pattern formation for a liquid crystal. Zbl 1187.82132
Golubitsky, Martin; Chillingworth, David
2003
The symmetry perspective. From equilibrium to chaos in phase space and physical space. Zbl 1031.37001
Golubitsky, Martin; Stewart, Ian
2002
What geometric visual hallucinations tell us about the visual cortex. Zbl 1037.91083
Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.; Wiener, Matthew C.
2002
Patterns of oscillation in coupled cell systems. Zbl 1017.37045
Golubitsky, Martin; Stewart, Ian
2002
Models of central pattern generators for quadruped locomotion. I: Primary gaits. Zbl 1039.92007
Buono, Pietro-Luciano; Golubitsky, Martin
2001
Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex. Zbl 1017.37025
Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.
2001
An unfolding theory approach to bursting in fast-slow systems. Zbl 1215.34043
Golubitsky, Martin; Josić, Krešimir; Kaper, Tasso J.
2001
Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford. Zbl 0956.00057
Golubitsky, M. (ed.); Knobloch, E. (ed.)
2000
Heteroclinic cycles in rings of coupled cells. Zbl 1011.34035
Buono, Pietro-Luciano; Golubitsky, Martin; Palacios, Antonio
2000
Hopf bifurcation from rotating waves and patterns in physical space. Zbl 0988.76036
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
2000
Target patterns and spirals in planar reaction-diffusion systems. Zbl 0965.35084
Golubitsky, M.; Knobloch, E.; Stewart, I.
2000
Symmetry and pattern formation in coupled cell networks. Zbl 0987.37041
Golubitsky, Martin; Stewart, Ian
1999
Symmetry, generic bifurcations, and mode interaction in nonlinear railway dynamics. Zbl 0981.70017
Nordstrøm Jensen, Carsten; Golubitsky, Martin; True, Hans
1999
Heteroclinic cycles in systems with $$D_n$$ symmetry. Zbl 0981.34030
Buono, Pietro-Luciano; Golubitsky, Martin; Palacios, Antonio
1999
Linear algebra and differential equations using MATLAB. Zbl 1329.00009
Golubitsky, Martin; Dellnitz, Michael
1999
A modular network for legged locomotion. Zbl 1039.92009
Golubitsky, Martin; Stewart, Ian; Buono, Pietro-Luciano; Collins, J. J.
1998
Meandering of the spiral tip: an alternative approach. Zbl 0902.58025
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
1997
An example of symmetry breaking to heteroclinic cycles. Zbl 0991.34043
Hou, Chuanze; Golubitsky, Martin
1997
Patterns in square arrays of coupled cells. Zbl 0889.34033
Gillis, David; Golubitsky, Martin
1997
A formula for a symmetry detective. Zbl 0933.37046
Gillis, D.; Golubitsky, M.
1997
Coupled cells with internal symmetry. I: Wreath products. Zbl 0894.58049
Dionne, Benoit; Golubitsky, Martin; Stewart, Ian
1996
Coupled cells with internal symmetry. II: Direct products. Zbl 0894.58050
Dionne, Benoit; Golubitsky, Martin; Stewart, Ian
1996
Symmetries of periodic solutions for planar potential systems. Zbl 0867.34030
Golubitsky, Martin; Mao, Jian-Min; Nicol, Matthew
1996
Symmetry in chaos: a search for pattern in mathematics, art and nature. Papeback ed. Zbl 0853.58002
Field, Michael; Golubitsky, Martin
1996
The constrained Liapunov-Schmidt procedure and periodic orbits. Zbl 0833.58014
Golubitsky, Martin; Marsden, Jerrold E.; Stewart, Ian; Dellnitz, Michael
1995
Cycling chaos. Zbl 0886.58077
Dellnitz, Michael; Field, Michael; Golubitsky, Martin; Ma, Jun; Hohmann, Andreas
1995
Symmetry detectives for SBR attractors. Zbl 0838.34055
Golubitsky, Martin; Nicol, Matthew
1995
Spirals in scalar reaction-diffusion equations. Zbl 0886.58102
Dellnitz, Michael; Golubitsky, Martin; Hohmann, Andreas; Stewart, Ian
1995
Symmetric chaos: how and why. Zbl 1042.37507
Field, Mike; Golubitsky, Martin
1995
Time-periodic spatially periodic planforms in Euclidean equivariant partial differential equations. Zbl 0851.35108
Dionne, Benoit; Golubitsky, Martin; Silber, Mary; Stewart, Ian
1995
Symmetry of attractors and the Karhunen-Loève decomposition. Zbl 0806.76087
Dellnitz, Michael; Golubitsky, Martin; Nicol, Matthew
1994
Coupled cells: Wreath products and direct products. Zbl 0810.34028
Golubitsky, Martin; Stewart, Ian; Dionne, Benoit
1994
A note on symmetries of invariant sets with compact group actions. Zbl 0813.58008
Field, Michael; Golubitsky, Martin; Nicol, Matthew
1994
The structure of symmetric attractors. Zbl 0805.58043
Melbourne, Ian; Dellnitz, Michael; Golubitsky, Martin
1993
Detecting the symmetry of attractors. Zbl 0783.58042
Barany, Ernest; Dellnitz, Michael; Golubitsky, Martin
1993
Symmetric patterns in linear arrays of coupled cells. Zbl 1055.80505
Epstein, Irving R.; Golubitsky, Martin
1993
An algebraic criterion for symmetric Hopf bifurcation. Zbl 0788.58038
Golubitsky, Martin; Stewart, Ian
1993
Fearful Symmetry: Is God a Geometer? Zbl 0784.00011
Stewart, Ian; Golubitsky, Martin
1993
Symmetry in chaos. A search for pattern in mathematics, art and nature. Zbl 0765.58001
Field, Michael; Golubitsky, Martin
1992
Planforms in two and three dimensions. Zbl 0774.35055
Dionne, Benoit; Golubitsky, Martin
1992
Fearful symmetry: is God a geometer? Zbl 0931.00014
Stewart, Ian; Golubitsky, Martin
1992
Mechanisms of symmetry creation. Zbl 0803.35011
Dellnitz, Michael; Golubitsky, Martin; Melbourne, Ian
1992
Bifurcations with local gauge symmetries in the Ginzburg-Landau equations. Zbl 0758.35073
Barany, Ernest; Golubitsky, Martin; Turski, Jacek
1992
Rotating chemical waves in the Gary-Scott model. Zbl 0745.58041
Farr, W. W.; Golubitsky, M.
1992
Bifurcation and symmetry. Cross influence between mathematics and applications. Proceedings of a workshop, held Marburg, Germany, June, 2- 14, 1991. Zbl 0745.00023
Allgower, Eugene L. (ed.); Böhmer, Klaus (ed.); Golubitsky, Martin (ed.)
1992
Coupled arrays of Josephson junctions and bifurcation of maps with $$S_ N$$ symmetry. Zbl 0803.58040
Aronson, D. G.; Golubitsky, Martin; Krupa, Martin
1991
Ponies on a merry-go-round in large arrays of Josephson junctions. Zbl 0732.58031
Aronson, D. G.; Golubitsky, Martin; Mallet-Paret, John
1991
Boundary conditions as symmetry constraints. Zbl 0735.35007
Crawford, J. D.; Golubitsky, M.; Gomes, M. G. M.; Knobloch, E.; Stewart, I. N.
1991
Time-reversibility and particle sedimentation. Zbl 0717.58049
Golubitsky, Martin; Krupa, Martin; Lim, Chjan
1991
Bifurcations on hemispheres. Zbl 0791.35044
Field, M.; Golubitsky, M.; Stewart, I.
1991
A torus bifurcation theorem with symmetry. Zbl 0695.34041
van Gils, S. A; Golubitsky, M.
1990
Heteroclinic cycles involving periodic solutions in mode interactions with $$O(2)$$ symmetry. Zbl 0737.58042
Melbourne, I.; Chossat, P.; Golubitsky, M.
1989
...and 46 more Documents
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#### Cited by 3,023 Authors

 64 Stewart, Ian Nicholas 57 Golubitsky, Martin A. 30 Ashwin, Peter 28 Guo, Shangjiang 24 Knobloch, Edgar 20 Chossat, Pascal 20 Melbourne, Ian 19 Dias, Ana Paula S. 18 Lamb, Jeroen S. W. 17 Ikeda, Kiyohiro 17 Marsden, Jerrold Eldon 16 Buono, Pietro-Luciano 16 Krawcewicz, Wieslaw Z. 15 Izumiya, Shyuichi 15 Labouriau, Isabel S. 14 Aguiar, Manuela A. D. 14 Chen, Yushu 14 Dangelmayr, Gerhard 14 Zhang, Chunrui 13 Gaeta, Giuseppe 13 Ha, Seung-Yeal 12 Field, Michael J. 12 Krupa, Martin 12 Saeki, Osamu 12 Schaeffer, David G. 11 Balanov, Zalman I. 11 Broer, Henk W. 11 Healey, Timothy J. 11 Wu, Jianhong 10 Antoneli, Fernando jun. 10 Bridges, Thomas J. 10 Chien, Cheng-Sheng 10 Lauterbach, Reiner 10 Palacios, Antonio 10 Roberts, Richard Mark 10 Romero-Fuster, María Carmen 9 Aston, Philip J. 9 Bressloff, Paul C. 9 Castro, Sofia B. S. D. 9 Chung, Kwok-Wai 9 Dellnitz, Michael 9 Janeczko, Stanisław 9 Laing, Carlo R. 9 Manoel, Miriam 9 Silber, Mary 9 Tchoń, Krzysztof 9 Zheng, Baodong 8 Atanackovic, Teodor M. 8 Greenleaf, Allan 8 Mei, Zhen 8 Pinto, Carla M. A. 7 Furter, Jacques-Elie 7 Holmes, Philip J. 7 Janovský, Vladimír 7 Kevrekidis, Ioannis George 7 Kielhöfer, Hansjörg 7 Kossowski, Marek 7 Langford, William F. 7 Podvigina, Ol’ga Mikhaĭlovna 7 Poláčik, Peter 7 Qin, Wenxin 7 Sanders, Jan A. 7 Wallace, Rodrick 7 Yang, Zhonghua 6 Baptistelli, Patrícia H. 6 Crawford, John David 6 de Jesus, C. Mendes 6 Desroches, Mathieu 6 Gatermann, Karin 6 Kevrekidis, Panayotis G. 6 Keyfitz, Barbara Lee 6 LeBlanc, Victor G. 6 Maier-Paape, Stanislaus 6 Marques, Francisco 6 Medveď, Milan 6 Moehlis, Jeff 6 Moiola, Jorge Luis 6 Murota, Kazuo 6 Reiter, Clifford A. 6 Renardy, Yuriko Yamamuro 6 Rucklidge, Alastair M. 6 Sarti, Alessandro 6 Schecter, Stephen 6 Vianello, Maurizio 6 Wan, Yieh-Hei 6 Wulff, Claudia 5 Armbruster, Dieter 5 Auffray, Nicolas 5 Bick, Christian 5 Böhmer, Klaus 5 Champneys, Alan R. 5 Chan, Bernard S. 5 Chan, H. S. Y. 5 Chen, Guanrong 5 Chillingworth, D. R. J. 5 Cicogna, Giampaolo 5 Citti, Giovanna 5 Cliffe, K. Andrew 5 Damon, James Norman 5 El Naschie, Mohamed Saladin ...and 2,923 more Authors
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#### Cited in 386 Serials

 192 Physica D 108 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 95 Chaos 88 Journal of Differential Equations 52 Chaos, Solitons and Fractals 43 Transactions of the American Mathematical Society 42 Archive for Rational Mechanics and Analysis 40 Journal of Fluid Mechanics 40 Journal of Nonlinear Science 34 Journal of Mathematical Analysis and Applications 34 Nonlinear Dynamics 32 Dynamics and Stability of Systems 32 Nonlinear Analysis. Theory, Methods & Applications 30 Journal of Dynamics and Differential Equations 29 SIAM Journal on Applied Dynamical Systems 28 Mathematical Proceedings of the Cambridge Philosophical Society 27 Journal of Mathematical Biology 24 Journal of Mathematical Economics 23 Journal of Computational and Applied Mathematics 22 Dynamical Systems 21 Bulletin of Mathematical Biology 21 Applied Mathematics and Computation 19 ZAMP. Zeitschrift für angewandte Mathematik und Physik 19 Applied Mathematics and Mechanics. (English Edition) 19 Mathematical and Computer Modelling 19 Physics of Fluids 18 Journal of Mathematical Physics 17 Computer Methods in Applied Mechanics and Engineering 17 Topology and its Applications 16 Communications in Mathematical Physics 16 Journal of Geometry and Physics 16 Linear Algebra and its Applications 15 Advances in Mathematics 15 Journal of Difference Equations and Applications 15 Communications in Nonlinear Science and Numerical Simulation 14 Mathematical Biosciences 14 The Journal of Mathematical Neuroscience 13 Biological Cybernetics 13 Journal of Computational Physics 13 Journal of Economic Theory 13 Proceedings of the American Mathematical Society 13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 12 Physics Letters. A 12 Journal of Elasticity 12 Journal of Mathematical Sciences (New York) 12 Nonlinear Analysis. Real World Applications 12 Journal of Theoretical Biology 11 Nonlinearity 11 Journal of Soviet Mathematics 11 Mathematische Annalen 11 Systems & Control Letters 11 Bulletin of the American Mathematical Society. New Series 11 Discrete and Continuous Dynamical Systems 10 Acta Mechanica 10 Journal of Statistical Physics 10 Journal of Functional Analysis 10 Journal of Pure and Applied Algebra 9 Computers & Mathematics with Applications 9 Annales de l’Institut Fourier 9 Automatica 9 Functional Analysis and its Applications 9 Inventiones Mathematicae 9 Manuscripta Mathematica 9 Acta Applicandae Mathematicae 9 Annals of Global Analysis and Geometry 9 Journal of Computational Neuroscience 8 International Journal of Engineering Science 8 Journal of the Mechanics and Physics of Solids 8 Computing 8 Duke Mathematical Journal 8 Journal of Optimization Theory and Applications 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Mathematische Zeitschrift 7 Neural Computation 7 SIAM Journal on Mathematical Analysis 7 Annales de l’Institut Henri Poincaré. Physique Théorique 7 Mathematics and Mechanics of Solids 7 Abstract and Applied Analysis 7 Proceedings of the Steklov Institute of Mathematics 6 International Journal of Theoretical Physics 6 Letters in Mathematical Physics 6 Mathematical Methods in the Applied Sciences 6 Cahiers de Topologie et Géométrie Différentielle Catégoriques 6 Geometriae Dedicata 6 Theoretical Population Biology 6 Applied Mathematics Letters 6 MCSS. Mathematics of Control, Signals, and Systems 6 Communications in Partial Differential Equations 6 Qualitative Theory of Dynamical Systems 6 Journal of Fixed Point Theory and Applications 6 Journal of Singularities 6 Symmetry 5 Reports on Mathematical Physics 5 Rocky Mountain Journal of Mathematics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Mathematics and Computers in Simulation 5 Journal of Economic Dynamics & Control 5 Neural Networks 5 European Journal of Applied Mathematics ...and 286 more Serials
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#### Cited in 61 Fields

 756 Dynamical systems and ergodic theory (37-XX) 625 Ordinary differential equations (34-XX) 390 Partial differential equations (35-XX) 355 Biology and other natural sciences (92-XX) 332 Global analysis, analysis on manifolds (58-XX) 231 Fluid mechanics (76-XX) 163 Mechanics of deformable solids (74-XX) 134 Manifolds and cell complexes (57-XX) 132 Numerical analysis (65-XX) 131 Differential geometry (53-XX) 119 Systems theory; control (93-XX) 115 Mechanics of particles and systems (70-XX) 88 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 76 Operator theory (47-XX) 64 Computer science (68-XX) 59 Statistical mechanics, structure of matter (82-XX) 46 Several complex variables and analytic spaces (32-XX) 41 Operations research, mathematical programming (90-XX) 37 Combinatorics (05-XX) 35 Calculus of variations and optimal control; optimization (49-XX) 33 Algebraic geometry (14-XX) 32 Linear and multilinear algebra; matrix theory (15-XX) 32 Classical thermodynamics, heat transfer (80-XX) 32 Quantum theory (81-XX) 31 Group theory and generalizations (20-XX) 30 Information and communication theory, circuits (94-XX) 26 Topological groups, Lie groups (22-XX) 26 Difference and functional equations (39-XX) 23 Probability theory and stochastic processes (60-XX) 21 Optics, electromagnetic theory (78-XX) 20 Algebraic topology (55-XX) 17 Convex and discrete geometry (52-XX) 17 General topology (54-XX) 16 Commutative algebra (13-XX) 15 Integral equations (45-XX) 13 Measure and integration (28-XX) 13 Relativity and gravitational theory (83-XX) 12 General and overarching topics; collections (00-XX) 11 Real functions (26-XX) 10 Statistics (62-XX) 9 History and biography (01-XX) 9 Nonassociative rings and algebras (17-XX) 9 Functional analysis (46-XX) 8 Category theory; homological algebra (18-XX) 7 Functions of a complex variable (30-XX) 7 Geophysics (86-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 6 Geometry (51-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Integral transforms, operational calculus (44-XX) 5 Astronomy and astrophysics (85-XX) 3 Mathematical logic and foundations (03-XX) 3 Number theory (11-XX) 3 Approximations and expansions (41-XX) 2 Potential theory (31-XX) 2 Abstract harmonic analysis (43-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Mathematics education (97-XX)

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