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Author ID: field.michael-j Recent zbMATH articles by "Field, Michael J."
Published as: Field, Michael; Field, M. J.; Field, M.; Field, Michael J.
Documents Indexed: 65 Publications since 1970, including 10 Books
Co-Authors: 20 Co-Authors with 32 Joint Publications
738 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

51 Publications have been cited 562 times in 387 Documents Cited by Year
Equivariant dynamical systems. Zbl 0447.58029
Field, M. J.
52
1980
Stability of mixing and rapid mixing for hyperbolic flows. Zbl 1140.37004
Field, Michael; Melbourne, Ian; Török, Andrei
39
2007
Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation. Zbl 1254.37053
Aguiar, M.; Ashwin, P.; Dias, A.; Field, M.
37
2011
Heteroclinic networks in coupled cell systems. Zbl 0947.37012
Ashwin, Peter; Field, Michael
32
1999
Lectures on bifurcations, dynamics and symmetry. Zbl 0857.58013
Field, Michael
31
1996
Combinatorial dynamics. Zbl 1058.37008
Field, Michael
30
2004
Dynamics and symmetry. Zbl 1146.34001
Field, Michael J.
27
2007
A refinement of the arithmetic mean-geometric mean inequality. Zbl 0392.26010
Cartwright, D. I.; Field, M. J.
26
1978
Heteroclinic networks in homogeneous and heterogeneous identical cell systems. Zbl 1371.37083
Field, M. J.
23
2015
Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions. Zbl 1140.37315
Field, Michael; Melbourne, Ian; Török, Andrew
22
2003
Symmetry in chaos. A search for pattern in mathematics, art and nature. Zbl 0765.58001
Field, Michael; Golubitsky, Martin
21
1992
Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups. Zbl 0824.58017
Field, M. J.; Richardson, R. W.
20
1989
Transversality in G-manifolds. Zbl 0318.57046
Field, M. J.
18
1977
Cycling chaos. Zbl 0886.58077
Dellnitz, Michael; Field, Michael; Golubitsky, Martin; Ma, Jun; Hohmann, Andreas
13
1995
Stable ergodicity of skew extensions by compact Lie groups. Zbl 0924.58045
Field, Michael; Parry, William
13
1999
Symmetric attractors for diffeomorphisms and flows. Zbl 0852.58074
Field, Michael; Melbourne, Ian; Nicol, Matthew
12
1996
Equivariant dynamical systems. Zbl 0205.28204
Field, M.
12
1970
Symmetry in chaos: a search for pattern in mathematics, art and nature. 2nd ed. Zbl 1173.37001
Field, Michael; Golubitsky, Martin
11
2009
Dynamical equivalence of networks of coupled dynamical systems. I: Asymmetric inputs. Zbl 1197.37017
Agarwal, N.; Field, M.
11
2010
Asynchronous networks and event driven dynamics. Zbl 1361.34011
Bick, Christian; Field, Michael
10
2017
Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets. Zbl 1076.37016
Field, Michael; Melbourne, Ian; Török, Andrei
10
2005
Symmetry breaking and branching patterns in equivariant bifurcation theory. II. Zbl 0768.58011
Field, M. J.; Richardson, R. W.
10
1992
Dynamical equivalence of networks of coupled dynamical systems. II: General case. Zbl 1197.37018
Agarwal, N.; Field, M.
10
2010
Symmetry breaking for compact Lie groups. Zbl 0851.58008
Field, Michael
8
1996
Bifurcations on hemispheres. Zbl 0791.35044
Field, M.; Golubitsky, M.; Stewart, I.
8
1991
Symmetry breaking in equivariant bifurcation problems. Zbl 0703.58044
Field, M. J.; Richardson, R. W.
8
1990
Patterns of desynchronization and resynchronization in heteroclinic networks. Zbl 1361.37075
Field, M. J.
7
2017
Symmetry-breaking and branching patterns in equivariant bifurcation theory. I. Zbl 0760.58008
Field, M. J.; Richardson, R. W.
7
1992
Ergodic theory of equivariant diffeomorphisms: Markov partitions and stable ergodicity. Zbl 1073.37030
Field, Michael; Nicol, Matthew
7
2004
Phase resetting effects for robust cycles between chaotic sets. Zbl 1080.37518
Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob
6
2003
Asynchronous networks: modularization of dynamics theorem. Zbl 1361.34012
Bick, Christian; Field, Michael
5
2017
Symmetry breaking for equivariant maps. Zbl 0882.57030
Field, Michael
5
1997
Generating sets for compact semisimple Lie groups. Zbl 0924.22013
Field, Michael
5
1999
Product dynamics for homoclinic attractors. Zbl 1145.37307
Ashwin, Peter; Field, Michael
5
2005
Stratifications of equivariant varieties. Zbl 0362.58003
Field, M. J.
5
1977
Equivariant dynamics. Zbl 0604.58044
Field, M. J.
4
1986
Dynamics near the product of planar heteroclinic attractors. Zbl 1253.37034
Agarwal, Nikita; Rodrigues, Alexandre; Field, Michael
4
2011
Handlebody decompositions for G-manifolds. Zbl 0472.57024
Field, M. J.
2
1982
Differential calculus and its applications. Zbl 0356.26005
Field, Michael J.
2
1976
Equivariant diffeomorphisms hyperbolic transverse to a G-action. Zbl 0491.58018
Field, M. J.
2
1983
Symmetry & critical points for a model shallow neural network. Zbl 1491.37049
Arjevani, Yossi; Field, Michael
2
2021
Heteroclinic cycles in symmetrically coupled systems. Zbl 0985.37048
Field, Michael
1
1999
Stable topological transitivity of skew and principal extensions. Zbl 1067.37035
Field, Michael; Niţică, Viorel
1
2001
Symmetry in chaos: a search for pattern in mathematics, art and nature. Papeback ed. Zbl 0853.58002
Field, Michael; Golubitsky, Martin
1
1996
Holomorphic function theory and complex manifolds. Zbl 0306.32001
Field, M. J.
1
1974
Sheaf cohomology, structures on manifolds and vanishing theory. Zbl 0306.32006
Field, M. J.
1
1974
Several complex variables. Zbl 0353.32001
Field, M. J.
1
1976
Isotopy and stability of equivariant diffeomorphisms. Zbl 0491.58019
Field, M. J.
1
1983
Resolving actions of compact Lie groups. Zbl 0382.57018
Field, M. J.
1
1978
Feedforward networks: adaptation, feedback, and synchrony. Zbl 1418.34106
Aguiar, Manuela A. D.; Dias, Ana; Field, Michael
1
2019
Essential real analysis. Zbl 1379.26001
Field, Michael
1
2017
Symmetry & critical points for a model shallow neural network. Zbl 1491.37049
Arjevani, Yossi; Field, Michael
2
2021
Feedforward networks: adaptation, feedback, and synchrony. Zbl 1418.34106
Aguiar, Manuela A. D.; Dias, Ana; Field, Michael
1
2019
Asynchronous networks and event driven dynamics. Zbl 1361.34011
Bick, Christian; Field, Michael
10
2017
Patterns of desynchronization and resynchronization in heteroclinic networks. Zbl 1361.37075
Field, M. J.
7
2017
Asynchronous networks: modularization of dynamics theorem. Zbl 1361.34012
Bick, Christian; Field, Michael
5
2017
Essential real analysis. Zbl 1379.26001
Field, Michael
1
2017
Heteroclinic networks in homogeneous and heterogeneous identical cell systems. Zbl 1371.37083
Field, M. J.
23
2015
Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation. Zbl 1254.37053
Aguiar, M.; Ashwin, P.; Dias, A.; Field, M.
37
2011
Dynamics near the product of planar heteroclinic attractors. Zbl 1253.37034
Agarwal, Nikita; Rodrigues, Alexandre; Field, Michael
4
2011
Dynamical equivalence of networks of coupled dynamical systems. I: Asymmetric inputs. Zbl 1197.37017
Agarwal, N.; Field, M.
11
2010
Dynamical equivalence of networks of coupled dynamical systems. II: General case. Zbl 1197.37018
Agarwal, N.; Field, M.
10
2010
Symmetry in chaos: a search for pattern in mathematics, art and nature. 2nd ed. Zbl 1173.37001
Field, Michael; Golubitsky, Martin
11
2009
Stability of mixing and rapid mixing for hyperbolic flows. Zbl 1140.37004
Field, Michael; Melbourne, Ian; Török, Andrei
39
2007
Dynamics and symmetry. Zbl 1146.34001
Field, Michael J.
27
2007
Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets. Zbl 1076.37016
Field, Michael; Melbourne, Ian; Török, Andrei
10
2005
Product dynamics for homoclinic attractors. Zbl 1145.37307
Ashwin, Peter; Field, Michael
5
2005
Combinatorial dynamics. Zbl 1058.37008
Field, Michael
30
2004
Ergodic theory of equivariant diffeomorphisms: Markov partitions and stable ergodicity. Zbl 1073.37030
Field, Michael; Nicol, Matthew
7
2004
Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions. Zbl 1140.37315
Field, Michael; Melbourne, Ian; Török, Andrew
22
2003
Phase resetting effects for robust cycles between chaotic sets. Zbl 1080.37518
Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob
6
2003
Stable topological transitivity of skew and principal extensions. Zbl 1067.37035
Field, Michael; Niţică, Viorel
1
2001
Heteroclinic networks in coupled cell systems. Zbl 0947.37012
Ashwin, Peter; Field, Michael
32
1999
Stable ergodicity of skew extensions by compact Lie groups. Zbl 0924.58045
Field, Michael; Parry, William
13
1999
Generating sets for compact semisimple Lie groups. Zbl 0924.22013
Field, Michael
5
1999
Heteroclinic cycles in symmetrically coupled systems. Zbl 0985.37048
Field, Michael
1
1999
Symmetry breaking for equivariant maps. Zbl 0882.57030
Field, Michael
5
1997
Lectures on bifurcations, dynamics and symmetry. Zbl 0857.58013
Field, Michael
31
1996
Symmetric attractors for diffeomorphisms and flows. Zbl 0852.58074
Field, Michael; Melbourne, Ian; Nicol, Matthew
12
1996
Symmetry breaking for compact Lie groups. Zbl 0851.58008
Field, Michael
8
1996
Symmetry in chaos: a search for pattern in mathematics, art and nature. Papeback ed. Zbl 0853.58002
Field, Michael; Golubitsky, Martin
1
1996
Cycling chaos. Zbl 0886.58077
Dellnitz, Michael; Field, Michael; Golubitsky, Martin; Ma, Jun; Hohmann, Andreas
13
1995
Symmetry in chaos. A search for pattern in mathematics, art and nature. Zbl 0765.58001
Field, Michael; Golubitsky, Martin
21
1992
Symmetry breaking and branching patterns in equivariant bifurcation theory. II. Zbl 0768.58011
Field, M. J.; Richardson, R. W.
10
1992
Symmetry-breaking and branching patterns in equivariant bifurcation theory. I. Zbl 0760.58008
Field, M. J.; Richardson, R. W.
7
1992
Bifurcations on hemispheres. Zbl 0791.35044
Field, M.; Golubitsky, M.; Stewart, I.
8
1991
Symmetry breaking in equivariant bifurcation problems. Zbl 0703.58044
Field, M. J.; Richardson, R. W.
8
1990
Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups. Zbl 0824.58017
Field, M. J.; Richardson, R. W.
20
1989
Equivariant dynamics. Zbl 0604.58044
Field, M. J.
4
1986
Equivariant diffeomorphisms hyperbolic transverse to a G-action. Zbl 0491.58018
Field, M. J.
2
1983
Isotopy and stability of equivariant diffeomorphisms. Zbl 0491.58019
Field, M. J.
1
1983
Handlebody decompositions for G-manifolds. Zbl 0472.57024
Field, M. J.
2
1982
Equivariant dynamical systems. Zbl 0447.58029
Field, M. J.
52
1980
A refinement of the arithmetic mean-geometric mean inequality. Zbl 0392.26010
Cartwright, D. I.; Field, M. J.
26
1978
Resolving actions of compact Lie groups. Zbl 0382.57018
Field, M. J.
1
1978
Transversality in G-manifolds. Zbl 0318.57046
Field, M. J.
18
1977
Stratifications of equivariant varieties. Zbl 0362.58003
Field, M. J.
5
1977
Differential calculus and its applications. Zbl 0356.26005
Field, Michael J.
2
1976
Several complex variables. Zbl 0353.32001
Field, M. J.
1
1976
Holomorphic function theory and complex manifolds. Zbl 0306.32001
Field, M. J.
1
1974
Sheaf cohomology, structures on manifolds and vanishing theory. Zbl 0306.32006
Field, M. J.
1
1974
Equivariant dynamical systems. Zbl 0205.28204
Field, M.
12
1970
all top 5

Cited by 466 Authors

29 Melbourne, Ian
23 Ashwin, Peter
19 Aguiar, Manuela A. D.
18 Dias, Ana Paula S.
16 Field, Michael J.
16 Stewart, Ian Nicholas
9 Lamb, Jeroen S. W.
9 Nicol, Matthew
9 Rodrigues, Alexandre A. P.
8 Golubitsky, Martin A.
7 Bick, Christian
7 Chossat, Pascal
7 Gaeta, Giuseppe
7 Rucklidge, Alastair M.
6 Araújo, Vítor
6 Fassò, Francesco
6 Török, Andrei
5 Labouriau, Isabel S.
5 Lauterbach, Reiner
5 Nijholt, Eddie
5 Postlethwaite, Claire M.
5 Rink, Bob W.
5 Varandas, Paulo
4 Buono, Pietro-Luciano
4 Butterley, Oliver
4 Castro, Sofia B. S. D.
4 Dragičević, Davor
4 Niţică, Viorel
4 Palacios, Antonio
4 Richardson, Roger Wolcott
4 Sanders, Jan A.
4 Sansonetto, Nicola
4 Walcher, Sebastian
4 Zhang, Wenmeng
3 Afraimovich, Valentin S.
3 Boyle, Mike
3 Chawanya, Tsuyoshi
3 Chung, Kwok-Wai
3 Cvitanović, Predrag
3 Gao, Peng
3 García-Naranjo, Luis C.
3 Gottwald, Georg A.
3 Hafouta, Yeor
3 Homburg, Ale Jan
3 Lu, Jian
3 Manoel, Miriam
3 Mercer, A. McD.
3 Ruan, Haibo
3 Schwenker, Sören Niklas
3 Soares, Pedro Tiago da Costa
3 Sturman, Rob
3 Terhesiu, Dalia
3 Wulff, Claudia
3 Zhang, Weinian
3 Zou, Yuru
2 Agarwal, Nikita
2 Aldaz, Jésus Munárriz
2 Aminzare, Zahra
2 Antoneli, Fernando jun.
2 Balanov, Zalman I.
2 Bálint, Péter
2 Belabbas, Mohamed-Ali
2 Bessa, Mário
2 Budanur, Nazmi Burak
2 Chen, Xudong
2 Danca, Marius-Florin
2 de Simoi, Jacopo
2 de Sousa, Robert
2 Dolgopyat, Dmitry
2 Dragomir, Sever Silvestru
2 Gomes, M. Gabriela M.
2 Holmes, Philip J.
2 Kirk, Vivien
2 Krawcewicz, Wieslaw Z.
2 Kühn, Christian
2 Lari-Lavassani, Ali
2 Lewis, Debra
2 Li, Wenxia
2 Liverani, Carlangelo
2 Luzzatto, Stefano
2 Merlevède, Florence
2 Minhós, Feliz Manuel
2 Ortega, Juan-Pablo
2 Parker, M. J.
2 Peixe, Telmo
2 Pikovsky, Arkady S.
2 Podvigina, Ol’ga Mikhaĭlovna
2 Poignard, Camille
2 Rabinovich, Mikhail I.
2 Rachinskii, Dmitrii I.
2 Ratiu, Tudor Stefan
2 Reiter, Clifford A.
2 Roberts, Richard Mark
2 Scheurle, Jürgen
2 Sharp, Richard W.
2 Trindade, Edvan
2 Tsujii, Masato
2 Vaienti, Sandro
2 Valls Anglés, Cláudia
2 Walkden, C. P.
...and 366 more Authors
all top 5

Cited in 137 Serials

25 Physica D
19 Journal of Nonlinear Science
18 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
17 Chaos
15 Nonlinearity
15 Journal of Differential Equations
15 Dynamical Systems
12 Ergodic Theory and Dynamical Systems
12 Journal of Dynamics and Differential Equations
11 Transactions of the American Mathematical Society
8 SIAM Journal on Applied Dynamical Systems
7 Archive for Rational Mechanics and Analysis
7 Communications in Mathematical Physics
5 Israel Journal of Mathematics
5 Journal of Mathematical Analysis and Applications
5 Chaos, Solitons and Fractals
5 Statistics & Probability Letters
5 Dynamics and Stability of Systems
4 Journal of Statistical Physics
4 Bulletin of the American Mathematical Society. New Series
4 Regular and Chaotic Dynamics
3 Mathematical Proceedings of the Cambridge Philosophical Society
3 Rocky Mountain Journal of Mathematics
3 Advances in Mathematics
3 The Annals of Probability
3 Journal of Computational and Applied Mathematics
3 Mathematische Annalen
3 Proceedings of the American Mathematical Society
3 Acta Applicandae Mathematicae
3 SIAM Review
3 Fractals
3 Discrete and Continuous Dynamical Systems
3 Communications in Nonlinear Science and Numerical Simulation
3 Journal of Mathematics and the Arts
2 Bulletin of the Australian Mathematical Society
2 International Journal of Theoretical Physics
2 Journal of Fluid Mechanics
2 Letters in Mathematical Physics
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Journal of Geometry and Physics
2 Automatica
2 Journal of Algebra
2 Journal of Pure and Applied Algebra
2 SIAM Journal on Control and Optimization
2 Communications in Statistics. Theory and Methods
2 SIAM Journal on Mathematical Analysis
2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
2 Journal of Inequalities and Applications
2 Journal of the European Mathematical Society (JEMS)
2 Annales Henri Poincaré
2 Qualitative Theory of Dynamical Systems
2 Portugaliae Mathematica. Nova Série
2 Quantum Information Processing
2 Journal of Mathematical Inequalities
2 Symmetry
2 The Journal of Mathematical Neuroscience
2 Nonlinear Analysis. Theory, Methods & Applications
1 Artificial Intelligence
1 Journal of Mathematical Biology
1 Journal of Mathematical Physics
1 Mathematical Biosciences
1 Mathematical Notes
1 Physica A
1 Physics Letters. A
1 Physics Reports
1 Bulletin of Mathematical Biology
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Aplikace Matematiky
1 Applied Mathematics and Computation
1 Archiv der Mathematik
1 Commentarii Mathematici Helvetici
1 Functional Analysis and its Applications
1 Illinois Journal of Mathematics
1 International Journal of Mathematics and Mathematical Sciences
1 International Journal of Game Theory
1 Inventiones Mathematicae
1 Journal of the Mathematical Society of Japan
1 Journal of Soviet Mathematics
1 Mathematische Zeitschrift
1 Memoirs of the American Mathematical Society
1 Monatshefte für Mathematik
1 Publications of the Research Institute for Mathematical Sciences, Kyoto University
1 Results in Mathematics
1 Topology and its Applications
1 Advances in Applied Mathematics
1 Probability Theory and Related Fields
1 Constructive Approximation
1 Revista Matemática Iberoamericana
1 Facta Universitatis. Series Mathematics and Informatics
1 Computational Mechanics
1 Journal of Theoretical Probability
1 Geometric and Functional Analysis. GAFA
1 Annals of Physics
1 Journal of Elasticity
1 Linear Algebra and its Applications
1 Proceedings of the National Academy of Sciences of the United States of America
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 Annales de l’Institut Henri Poincaré. Physique Théorique
1 Celestial Mechanics and Dynamical Astronomy
1 Indagationes Mathematicae. New Series
...and 37 more Serials
all top 5

Cited in 48 Fields

249 Dynamical systems and ergodic theory (37-XX)
117 Ordinary differential equations (34-XX)
43 Biology and other natural sciences (92-XX)
34 Probability theory and stochastic processes (60-XX)
25 Global analysis, analysis on manifolds (58-XX)
18 Manifolds and cell complexes (57-XX)
17 Real functions (26-XX)
17 Mechanics of particles and systems (70-XX)
15 Combinatorics (05-XX)
13 Partial differential equations (35-XX)
12 Computer science (68-XX)
12 Fluid mechanics (76-XX)
11 Systems theory; control (93-XX)
10 Quantum theory (81-XX)
9 Measure and integration (28-XX)
9 Statistical mechanics, structure of matter (82-XX)
9 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
8 Group theory and generalizations (20-XX)
8 Operator theory (47-XX)
7 Differential geometry (53-XX)
7 Numerical analysis (65-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
6 Topological groups, Lie groups (22-XX)
5 General and overarching topics; collections (00-XX)
5 Commutative algebra (13-XX)
5 General topology (54-XX)
5 Operations research, mathematical programming (90-XX)
5 Information and communication theory, circuits (94-XX)
4 Difference and functional equations (39-XX)
4 Convex and discrete geometry (52-XX)
4 Algebraic topology (55-XX)
4 Mechanics of deformable solids (74-XX)
3 Algebraic geometry (14-XX)
3 Optics, electromagnetic theory (78-XX)
2 History and biography (01-XX)
2 Number theory (11-XX)
2 Functions of a complex variable (30-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Astronomy and astrophysics (85-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Associative rings and algebras (16-XX)
1 Category theory; homological algebra (18-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Integral transforms, operational calculus (44-XX)
1 Functional analysis (46-XX)
1 Geometry (51-XX)
1 Statistics (62-XX)
1 Classical thermodynamics, heat transfer (80-XX)

Citations by Year