## Abraham, Ralph Herman

Compute Distance To:
 Author ID: abraham.ralph-herman Published as: Abraham, Ralph; Abraham, Ralph H.; Abraham, R.; Abraham, Ralph Herman more...less Homepage: http://www.ralph-abraham.org/ External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 51 Publications since 1962, including 13 Books 1 Contribution as Editor Co-Authors: 47 Co-Authors with 30 Joint Publications 1,385 Co-Co-Authors
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### Co-Authors

 21 single-authored 5 Marsden, Jerrold Eldon 4 Shaw, Christopher D. 4 Ueda, Yoshisuke 3 Gardini, Laura 3 Stewart, H. Bruce 2 Abraham, Frederick David 2 Ratiu, Tudor Stefan 1 Amano, Hiroyuki 1 Bischi, Gian-Italo 1 Carroll, Thomas L. 1 Corliss, John B. 1 Dorband, John E. 1 Fournier-Prunaret, Danièle 1 Friedman, Dan 1 Gilmore, Robert 1 Glass, Leon 1 Grebogi, Celso 1 Hirano, Makoto 1 Holmes, Philip J. 1 Jas, Frank 1 Keith, Alexander 1 Kocak, Huseyin 1 Koebbe, Matthew 1 Letellier, Christophe 1 Lozi, René 1 Mayer-Kress, Gottfried 1 McKenna, Terence 1 Mira, Christian 1 Ohta, Hirofumi 1 Olsen, Lars Folke 1 Parlitz, Ulrich 1 Pecora, Louis M. 1 Pikovsky, Arkady S. 1 Record, Ronald J. 1 Robbin, Joel William 1 Rossler, Otto E. 1 Roy, Sisir 1 Russell, Willard 1 Scott, Katherine A. 1 Shaw, Christopher C. 1 Sheldrake, Rupert 1 Shepelyansky, Dima L. 1 Simó, Carles 1 Smale, Steve 1 Smith, William Robert 1 Tsuda, Ichiro 1 Ueda, Yoshinori
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### Serials

 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Grazer Mathematische Berichte 2 Journal of the Calcutta Mathematical Society 1 Physica D 1 Journal of Economic Dynamics & Control 1 Chaos 1 International Journal of Pure and Applied Mathematics 1 Bulletin of the American Mathematical Society 1 Journal of Mathematics and Mechanics 1 Publications du Département de Mathématiques 1 Applied Mathematical Sciences 1 World Scientific Series on Nonlinear Science. Series A
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### Fields

 37 Dynamical systems and ergodic theory (37-XX) 13 Global analysis, analysis on manifolds (58-XX) 7 Mechanics of particles and systems (70-XX) 5 General and overarching topics; collections (00-XX) 5 Computer science (68-XX) 4 History and biography (01-XX) 4 Ordinary differential equations (34-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Differential geometry (53-XX) 3 Biology and other natural sciences (92-XX) 2 Manifolds and cell complexes (57-XX) 2 Optics, electromagnetic theory (78-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX)

### Citations contained in zbMATH Open

27 Publications have been cited 1,742 times in 1,687 Documents Cited by Year
Foundations of mechanics. 2nd ed., rev., enl., and reset. With the assistance of Tudor Ratiu and Richard Cushman. Zbl 0393.70001
Abraham, Ralph; Marsden, Jerrold E.
1978
Manifolds, tensor analysis, and applications. 2nd ed. Zbl 0875.58002
Abraham, R.; Marsden, J. E.; Ratiu, T.
1988
Transversal mappings and flows. An appendix by Al Kelley. Zbl 0171.44404
Abraham, Ralph; Robbin, Joel
1967
Manifolds, tensor analysis, and applications. Zbl 0508.58001
Abraham, Ralph; Marsden, Jerrold E.; Ratiu, Tudor
1983
Transversality in manifolds of mappings. Zbl 0171.44501
Abraham, Ralph
1963
Nongenericity of $$\Omega$$-stability. Zbl 0215.25102
Abraham, R.; Smale, S.
1970
Foundations of mechanics. A mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the three-body problem. With the assistence of Jerrold E. Marsden. Zbl 0158.42901
Abraham, Ralph
1967
A double logistic map. Zbl 0870.58020
Gardini, Laura; Abraham, Ralph; Record, Ronald J.; Fournier-Prunaret, Daniele
1994
Bumpy metrics. Zbl 0215.23301
Abraham, R.
1970
Chaos in discrete dynamical systems: a visual introduction in 2 dimensions. Companion CD-ROM by Ronald J. Record and Ralph H. Abraham. Zbl 0883.58019
Abraham, Ralph H.; Gardini, Laura; Mira, Christian
1997
Hamiltonian mechanics on Lie groups and hydrodynamics. Zbl 0211.57402
Marsden, J.; Abraham, R.
1970
The chaos avant-garde. Memories of the early days of chaos theory. Zbl 0958.00013
2000
Chaostrophes, intermittency, and noise. Zbl 0577.58003
Abraham, Ralph H.
1985
A chaotic blue sky catastrophe in forced relaxation oscillations. Zbl 0602.58035
Abraham, Ralph H.; Stewart, H. Bruce
1986
Dynamics. The geometry of behavior. Part 1: Periodic behavior. Part 2: Chaotic behavior. Part 3: Global behavior. Part 4: Bifurcation behavior. 2nd ed. Zbl 0763.58001
Abraham, Ralph H.; Shaw, Christopher D.
1992
Dynamics - The geometry of behavior. Part 4: Bifurcation behavior. Zbl 0702.58001
Abraham, Ralph H.; Shaw, Christopher D.
1988
Nonlinear resonance in basin portraits of two coupled swings under periodic forcing. Zbl 0963.70551
Ueda, Yoshisuke; Ueda, Yoshinori; Stewart, H. Bruce; Abraham, Ralph H.
1998
Bubbles and crashes: gradient dynamics in financial markets. Zbl 1170.91442
Friedman, Daniel; Abraham, Ralph
2009
Some elements for a history of the dynamical systems theory. Zbl 1462.37002
Letellier, Christophe; Abraham, Ralph; Shepelyansky, Dima L.; Rössler, Otto E.; Holmes, Philip; Lozi, René; Glass, Leon; Pikovsky, Arkady; Olsen, Lars F.; Tsuda, Ichiro; Grebogi, Celso; Parlitz, Ulrich; Gilmore, Robert; Pecora, Louis M.; Carroll, Thomas L.
2021
Basin configuration of a six-dimensional model of an electric power system. Zbl 1044.37560
Ueda, Yoshisuke; Amano, Hiroyuki; Abraham, Ralph H.; Stewart, H. Bruce
2002
Is there chaos without noise? Zbl 0569.58023
Abraham, Ralph H.
1985
Visualization techniques for cellular dynamata. Zbl 0874.58026
Abraham, Ralph H.
1997
Attractor and basin portraits of a double swing power system. Zbl 1129.37364
Ueda, Yoshisuke; Hirano, Makoto; Ohta, Hirofumi; Abraham, Ralph H.
2004
Chaos, Gaia, Eros. A chaos pioneer uncovers the three great streams of history. Zbl 0878.00013
Abraham, Ralph H.
1994
Phase regulation of coupled oscillators and chaos. Zbl 0836.34036
Abraham, Ralph H.
1991
In pursuit of Birkhoff’s chaotic attractor. Zbl 0564.58023
Abraham, Ralph H.
1985
Piecewise differentiable manifolds and the space-time of general relativity. Zbl 0105.21202
Abraham, R.
1962
Some elements for a history of the dynamical systems theory. Zbl 1462.37002
Letellier, Christophe; Abraham, Ralph; Shepelyansky, Dima L.; Rössler, Otto E.; Holmes, Philip; Lozi, René; Glass, Leon; Pikovsky, Arkady; Olsen, Lars F.; Tsuda, Ichiro; Grebogi, Celso; Parlitz, Ulrich; Gilmore, Robert; Pecora, Louis M.; Carroll, Thomas L.
2021
Bubbles and crashes: gradient dynamics in financial markets. Zbl 1170.91442
Friedman, Daniel; Abraham, Ralph
2009
Attractor and basin portraits of a double swing power system. Zbl 1129.37364
Ueda, Yoshisuke; Hirano, Makoto; Ohta, Hirofumi; Abraham, Ralph H.
2004
Basin configuration of a six-dimensional model of an electric power system. Zbl 1044.37560
Ueda, Yoshisuke; Amano, Hiroyuki; Abraham, Ralph H.; Stewart, H. Bruce
2002
The chaos avant-garde. Memories of the early days of chaos theory. Zbl 0958.00013
2000
Nonlinear resonance in basin portraits of two coupled swings under periodic forcing. Zbl 0963.70551
Ueda, Yoshisuke; Ueda, Yoshinori; Stewart, H. Bruce; Abraham, Ralph H.
1998
Chaos in discrete dynamical systems: a visual introduction in 2 dimensions. Companion CD-ROM by Ronald J. Record and Ralph H. Abraham. Zbl 0883.58019
Abraham, Ralph H.; Gardini, Laura; Mira, Christian
1997
Visualization techniques for cellular dynamata. Zbl 0874.58026
Abraham, Ralph H.
1997
A double logistic map. Zbl 0870.58020
Gardini, Laura; Abraham, Ralph; Record, Ronald J.; Fournier-Prunaret, Daniele
1994
Chaos, Gaia, Eros. A chaos pioneer uncovers the three great streams of history. Zbl 0878.00013
Abraham, Ralph H.
1994
Dynamics. The geometry of behavior. Part 1: Periodic behavior. Part 2: Chaotic behavior. Part 3: Global behavior. Part 4: Bifurcation behavior. 2nd ed. Zbl 0763.58001
Abraham, Ralph H.; Shaw, Christopher D.
1992
Phase regulation of coupled oscillators and chaos. Zbl 0836.34036
Abraham, Ralph H.
1991
Manifolds, tensor analysis, and applications. 2nd ed. Zbl 0875.58002
Abraham, R.; Marsden, J. E.; Ratiu, T.
1988
Dynamics - The geometry of behavior. Part 4: Bifurcation behavior. Zbl 0702.58001
Abraham, Ralph H.; Shaw, Christopher D.
1988
A chaotic blue sky catastrophe in forced relaxation oscillations. Zbl 0602.58035
Abraham, Ralph H.; Stewart, H. Bruce
1986
Chaostrophes, intermittency, and noise. Zbl 0577.58003
Abraham, Ralph H.
1985
Is there chaos without noise? Zbl 0569.58023
Abraham, Ralph H.
1985
In pursuit of Birkhoff’s chaotic attractor. Zbl 0564.58023
Abraham, Ralph H.
1985
Manifolds, tensor analysis, and applications. Zbl 0508.58001
Abraham, Ralph; Marsden, Jerrold E.; Ratiu, Tudor
1983
Foundations of mechanics. 2nd ed., rev., enl., and reset. With the assistance of Tudor Ratiu and Richard Cushman. Zbl 0393.70001
Abraham, Ralph; Marsden, Jerrold E.
1978
Nongenericity of $$\Omega$$-stability. Zbl 0215.25102
Abraham, R.; Smale, S.
1970
Bumpy metrics. Zbl 0215.23301
Abraham, R.
1970
Hamiltonian mechanics on Lie groups and hydrodynamics. Zbl 0211.57402
Marsden, J.; Abraham, R.
1970
Transversal mappings and flows. An appendix by Al Kelley. Zbl 0171.44404
Abraham, Ralph; Robbin, Joel
1967
Foundations of mechanics. A mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the three-body problem. With the assistence of Jerrold E. Marsden. Zbl 0158.42901
Abraham, Ralph
1967
Transversality in manifolds of mappings. Zbl 0171.44501
Abraham, Ralph
1963
Piecewise differentiable manifolds and the space-time of general relativity. Zbl 0105.21202
Abraham, R.
1962
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### Cited by 2,096 Authors

 31 Ratiu, Tudor Stefan 29 Marsden, Jerrold Eldon 16 de la Llave, Rafael 15 Llibre, Jaume 15 Martín de Diego, David 12 Forstnerič, Franc 12 Marmo, Giuseppe 10 Mardare, Cristinel 10 Simo, Juan Carlos 10 Smale, Steve 10 Svendsen, Bob 9 Ibort, Alberto 9 Kucharz, Wojciech 8 Alarcón, Antonio 8 Bloch, Anthony Michael 8 Brunovský, Pavol 8 Ciarlet, Philippe Gaston 8 de León Rodríguez, Manuel 8 Gardini, Laura 8 Prykarpatsky, Anatoliy Karolevych 7 Ciaglia, Florio Maria 7 Desbrun, Mathieu 7 Esen, Oğul 7 Gay-Balmaz, François 7 Krishnaprasad, P.s. 7 Lewis, Debra 7 Marrero, Juan Carlos 7 Muñoz-Lecanda, Miguel C. 7 Peralta-Salas, Daniel 7 Román-Roy, Narciso 7 Shub, Michael 7 Śniatycki, Jędrzej 7 van der Schaft, Arjan J. 6 Barretta, Raffaele 6 Bischi, Gian-Italo 6 Butscher, Adrian 6 Fischer, Arthur Elliot 6 Holm, Darryl Dallas 6 Lewis, Andrew D. 6 Ma, Jipu 6 Medveď, Milan 6 Ortega, Juan-Pablo 6 Patrick, George W. 6 Piccione, Paolo 6 Rabier, Patrick J. 6 Romano, Giovanni P. 5 Cariñena, José F. 5 Crovisier, Sylvain 5 Di Cosmo, Fabio 5 Enciso, Alberto 5 Fassò, Francesco 5 Frauenfelder, Urs Adrian 5 Fuchs, Gerard 5 Gauthier, Jean-Paul A. 5 Knauf, Andreas 5 Lacomba, Ernesto A. 5 Montgomery, Richard 5 Pappas, George J. 5 Poláčik, Peter 5 Pugh, Charles Chapman 5 Rasmussen, Martin 5 Robinson, Clark 5 Ṣahin, Bayram 5 Schmid, Rudolf 5 Tabuada, Paulo 5 Weinstein, Alan David 5 Yavari, Arash 5 Zhang, Shiqing 4 Adams, Malcolm R. 4 Allen, Beth 4 Barbero-Liñán, María 4 Bogolyubov, Nikolaĭ Nikolaevich jun. 4 Bordemann, Martin 4 Bullo, Francesco 4 Cheng, Daizhan 4 Chichilnisky, Graciela 4 Deprit, André 4 Diaco, Marina 4 Diacu, Florin Nicolae 4 Dobrokhotov, Sergei Yurievich 4 Fournier-Prunaret, Danièle 4 Gotay, Mark J. 4 Gràcia, Xavier 4 Guha, Partha 4 Guillemin, Victor W. 4 Hieber, Matthias 4 Holmes, Philip J. 4 Iwai, Toshihiro 4 Janeczko, Stanisław 4 Kopel, Michael 4 Kozono, Hideo 4 Leok, Melvin 4 Lopez Fernandez, Francisco Jose 4 Mallet-Paret, John Joseph 4 Marotto, Frederick R. 4 Meyer, Kenneth R. 4 Mira, Christian 4 Palha, Artur 4 Pérez-Pardo, Juan Manuel 4 Prykarpatsky, Yarema Anatoliyovych ...and 1,996 more Authors
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### Cited in 343 Serials

 72 Journal of Differential Equations 66 Communications in Mathematical Physics 52 Transactions of the American Mathematical Society 39 Journal of Mathematical Economics 37 International Journal of Theoretical Physics 36 Journal of Geometry and Physics 29 Journal of Mathematical Analysis and Applications 29 Proceedings of the American Mathematical Society 27 Archive for Rational Mechanics and Analysis 26 Journal of Nonlinear Science 24 Journal of Mathematical Physics 24 Mathematische Annalen 22 Physica D 20 Acta Mechanica 20 Journal of Dynamics and Differential Equations 19 Letters in Mathematical Physics 19 Chaos, Solitons and Fractals 18 Mathematische Zeitschrift 17 Advances in Mathematics 17 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 16 Journal of Functional Analysis 16 Regular and Chaotic Dynamics 15 Annals of Global Analysis and Geometry 15 Annales de l’Institut Henri Poincaré. Physique Théorique 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 13 Annales de l’Institut Fourier 13 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 13 Differential Geometry and its Applications 13 The Journal of Geometric Analysis 13 Celestial Mechanics and Dynamical Astronomy 13 Bulletin of the American Mathematical Society 12 Computer Methods in Applied Mechanics and Engineering 12 Inventiones Mathematicae 12 Acta Applicandae Mathematicae 12 MCSS. Mathematics of Control, Signals, and Systems 12 Journal of Geometric Mechanics 11 Journal of Computational Physics 11 Systems & Control Letters 11 Nonlinear Analysis. Theory, Methods & Applications 10 Journal of Economic Theory 10 International Journal of Geometric Methods in Modern Physics 10 Foundations of Physics 9 General Relativity and Gravitation 9 Reports on Mathematical Physics 9 Duke Mathematical Journal 9 Applied Mathematics and Mechanics. (English Edition) 9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Linear Algebra and its Applications 8 Czechoslovak Mathematical Journal 8 Monatshefte für Mathematik 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 SIAM Journal on Control and Optimization 8 Bulletin of the American Mathematical Society. New Series 8 Foundations of Computational Mathematics 7 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 7 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 7 Manuscripta Mathematica 7 Mathematical Systems Theory 7 Ergodic Theory and Dynamical Systems 7 Celestial Mechanics 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Nonlinear Dynamics 7 Acta Mathematica Sinica. English Series 6 Computers & Mathematics with Applications 6 Journal of Statistical Physics 6 Journal of Computational and Applied Mathematics 6 Numerische Mathematik 6 Annals of Physics 6 Journal of Mathematical Sciences (New York) 6 Chaos 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Bulletin of the Brazilian Mathematical Society. New Series 5 Astrophysics and Space Science 5 Mathematical Notes 5 Rocky Mountain Journal of Mathematics 5 Applied Mathematics and Computation 5 Automatica 5 BIT 5 Memoirs of the American Mathematical Society 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Journal of Economic Dynamics & Control 5 Journal of Elasticity 5 Calculus of Variations and Partial Differential Equations 5 Annales Henri Poincaré 5 SIAM Journal on Applied Dynamical Systems 4 Nonlinearity 4 Physics Letters. A 4 Theoretical and Mathematical Physics 4 Reviews in Mathematical Physics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Applied Mathematics and Optimization 4 Publications Mathématiques 4 Journal für die Reine und Angewandte Mathematik 4 Mathematics and Computers in Simulation 4 Mathematical Programming 4 Meccanica 4 Topology and its Applications 4 Circuits, Systems, and Signal Processing 4 Chinese Annals of Mathematics. Series B ...and 243 more Serials
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### Cited in 58 Fields

 586 Dynamical systems and ergodic theory (37-XX) 354 Differential geometry (53-XX) 349 Mechanics of particles and systems (70-XX) 278 Global analysis, analysis on manifolds (58-XX) 188 Partial differential equations (35-XX) 159 Ordinary differential equations (34-XX) 134 Quantum theory (81-XX) 102 Numerical analysis (65-XX) 97 Mechanics of deformable solids (74-XX) 88 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 83 Systems theory; control (93-XX) 80 Manifolds and cell complexes (57-XX) 72 Fluid mechanics (76-XX) 63 Operator theory (47-XX) 60 Calculus of variations and optimal control; optimization (49-XX) 54 Functional analysis (46-XX) 52 Topological groups, Lie groups (22-XX) 51 Several complex variables and analytic spaces (32-XX) 42 Relativity and gravitational theory (83-XX) 37 Statistical mechanics, structure of matter (82-XX) 32 Nonassociative rings and algebras (17-XX) 32 Algebraic topology (55-XX) 32 Probability theory and stochastic processes (60-XX) 31 Algebraic geometry (14-XX) 30 Operations research, mathematical programming (90-XX) 26 Biology and other natural sciences (92-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 22 Optics, electromagnetic theory (78-XX) 19 General topology (54-XX) 17 Computer science (68-XX) 17 Information and communication theory, circuits (94-XX) 16 Real functions (26-XX) 15 History and biography (01-XX) 15 Difference and functional equations (39-XX) 12 Statistics (62-XX) 11 Functions of a complex variable (30-XX) 10 Combinatorics (05-XX) 10 Category theory; homological algebra (18-XX) 8 Measure and integration (28-XX) 7 Group theory and generalizations (20-XX) 7 Geometry (51-XX) 6 Convex and discrete geometry (52-XX) 6 Geophysics (86-XX) 5 General and overarching topics; collections (00-XX) 5 Mathematical logic and foundations (03-XX) 5 Field theory and polynomials (12-XX) 5 Commutative algebra (13-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Approximations and expansions (41-XX) 4 Abstract harmonic analysis (43-XX) 4 Integral equations (45-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Astronomy and astrophysics (85-XX) 3 Number theory (11-XX) 3 Associative rings and algebras (16-XX) 3 $$K$$-theory (19-XX) 2 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX)

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