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## Arnaud, Marie-Claude

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 Author ID: arnaud.marie-claude Published as: Arnaud, M-C; Arnaud, M. C.; Arnaud, M.-C.; Arnaud, Marie-Claude Homepage: http://www.univ-avignon.fr/en/research/annuaire-chercheurs/membrestruc/personnel... External Links: MGP · Wikidata
 Documents Indexed: 45 Publications since 1989, including 1 Book
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#### Co-Authors

 38 single-authored 1 Arcostanzo, Marc 1 Audin, Michèle 1 Béguin, François 1 Berger, Pierre 1 Bolle, Philippe 1 Bonatti, Christian 1 Chéritat, Arnaud 1 Crovisier, Sylvain 1 Eliasson, L. Hakan 1 Ghys, Étienne 1 Hofer, Helmut H. W. 1 Kaloshin, Vadim Yu. 1 Le Calvez, Patrice 1 Le Roux, Frédéric 1 Lhuissier, Marie 1 Massot, Patrick 1 Rollet, Laurent 1 Venturelli, Andrea 1 Yoccoz, Jean-Christophe 1 Zavidovique, Maxime
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#### Serials

 6 Nonlinearity 5 Ergodic Theory and Dynamical Systems 3 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Mémoires de la Société Mathématique de France. Nouvelle Série 2 Comptes Rendus de l’Académie des Sciences. Série I 1 Communications in Mathematical Physics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin de la Société Mathématique de France 1 Gazette des Mathématiciens 1 Publications Mathématiques 1 Journal of Differential Equations 1 Mathematische Zeitschrift 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 Geometric and Functional Analysis. GAFA 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 Calculus of Variations and Partial Differential Equations 1 Discrete and Continuous Dynamical Systems 1 Publicaciones Matemáticas del Uruguay 1 Annals of Mathematics. Second Series 1 Regular and Chaotic Dynamics 1 Annales Henri Poincaré 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal of the Institute of Mathematics of Jussieu 1 Oberwolfach Reports 1 Journal of Modern Dynamics
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#### Fields

 40 Dynamical systems and ergodic theory (37-XX) 10 Differential geometry (53-XX) 10 Mechanics of particles and systems (70-XX) 4 Manifolds and cell complexes (57-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Partial differential equations (35-XX)

#### Citations contained in zbMATH Open

33 Publications have been cited 153 times in 100 Documents Cited by Year
The $$C^1$$ closing lemma. Zbl 0920.58039
Arnaud, Marie-Claude
1998
On a theorem due to Birkhoff. Zbl 1216.37020
Arnaud, Marie-Claude
2010
Generic symplectic dynamics. Zbl 1084.37017
Arnaud, Marie-Claude; Bonatti, Christian; Crovisier, Sylvain
2005
The link between the shape of the irrational Aubry-Mather sets and their Lyapunov exponents. Zbl 1257.37028
Arnaud, Marie-Claude
2011
Creation of connections in $$C^1$$-topology. Zbl 0997.37007
Arnaud, Marie-Claude
2001
The generic symplectic $$C^1$$-diffeomorphisms of four-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely elliptic periodic point. Zbl 1030.37037
Arnaud, Marie-Claude
2002
Green bundles and regularity of $$C^0$$-Lagrangians invariant graphs of Tonelli flows. Zbl 1143.70009
Arnaud, Marie-Claude
2008
Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures. Zbl 1269.37031
Arnaud, M.-C.
2012
Tonelli Hamiltonians without conjugate points and $$C^0$$ integrability. Zbl 1345.37063
Arcostanzo, M.; Arnaud, M.-C.; Bolle, P.; Zavidovique, M.
2015
Three results on the regularity of the curves that are invariant by an exact symplectic twist map. Zbl 1177.53070
Arnaud, M.-C.
2009
The non-hyperbolicity of irrational invariant curves for twist maps and all that follows. Zbl 1361.37046
Arnaud, Marie-Claude; Berger, Pierre
2016
Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting. Zbl 1269.37032
Arnaud, M.-C.
2013
A nondifferentiable essential irrational invariant curve for a $$C^1$$ symplectic twist map. Zbl 1276.37034
Arnaud, Marie-Claude
2011
The tiered Aubry set for autonomous Lagrangian functions. Zbl 1152.37025
Arnaud, Marie-Claude
2008
Pseudographs and the Lax-Oleinik semi-group: a geometric and dynamical interpretation. Zbl 1284.05120
Arnaud, M-C
2011
Boundaries of instability zones for symplectic twist maps. Zbl 1290.37024
Arnaud, M.-C.
2014
$$C^1$$-generic billiard tables have a dense set of periodic points. Zbl 1417.37094
Arnaud, Marie-Claude
2013
Green bundles and related topics. Zbl 1243.37037
Arnaud, Marie-Claude
2011
A particular minimization property implies $$C^{0}$$-integrability. Zbl 1214.37044
Arnaud, M.-C.
2011
Hyperbolic periodic orbits and Mather sets in certain symmetric cases. Zbl 1118.37030
Arnaud, M.-C.
2006
Convergence of the semi-group of Lax-Oleinik: a geometric point of view. Zbl 1181.37018
Arnaud, M. C.
2005
Approximation des ensembles $$\omega$$-limites des difféomorphismes par des orbites pério-diques. (Approximation of $$\omega$$-limit sets of diffeomorphisms by periodic orbits). Zbl 1024.37011
Arnaud, Marie-Claude
2003
Symplectic $$C^1$$-diffeomorphisms of 4-dimensional manifolds. Zbl 0964.37034
Arnaud, Marie-Claude
2000
Existence of completely elliptic periodic orbits of symmetric and convex Hamiltonians. Zbl 0943.37029
Arnaud, Marie-Claude
1999
On the type of certain periodic orbits minimizing the Lagrangian action. Zbl 0901.58013
Arnaud, Marie-Claude
1998
Creation of periodic points of all types in the neighbourhood of K.A.M. tori. Zbl 0853.58046
Arnaud, Marie-Claude
1995
Types of fixed points of symplectic diffeomorphisms on $$\mathbb{T}^ n\times \mathbb{R}^ n$$. Zbl 0758.58009
Arnaud, Marie-Claude
1992
Sur les points fixes des difféomorphismes exacts symplectiques de $$T^ n\times R^ n$$. (Fixed points of exact symplectic diffeomorphisms of $$T^ n\times R^ n)$$. Zbl 0696.57017
Arnaud, Marie-Claude
1989
Hyperbolicity for conservative twist maps of the 2-dimensional annulus. Zbl 1372.37087
Arnaud, Marie-Claude
2016
Lyapunov exponents for conservative twisting dynamics: a survey. Zbl 1362.37117
Arnaud, Marie-Claude
2016
When are the invariant submanifolds of symplectic dynamics Lagrangian? Zbl 1308.37026
Arnaud, Marie-Claude
2014
An “orbit closing lemma”. Zbl 0867.58040
Arnaud, Marie-Claude
1996
Type of critical points of Hamiltonian functions and of fixed points of symplectic diffeomorphisms. Zbl 0811.58022
Arnaud, Marie-Claude
1994
The non-hyperbolicity of irrational invariant curves for twist maps and all that follows. Zbl 1361.37046
Arnaud, Marie-Claude; Berger, Pierre
2016
Hyperbolicity for conservative twist maps of the 2-dimensional annulus. Zbl 1372.37087
Arnaud, Marie-Claude
2016
Lyapunov exponents for conservative twisting dynamics: a survey. Zbl 1362.37117
Arnaud, Marie-Claude
2016
Tonelli Hamiltonians without conjugate points and $$C^0$$ integrability. Zbl 1345.37063
Arcostanzo, M.; Arnaud, M.-C.; Bolle, P.; Zavidovique, M.
2015
Boundaries of instability zones for symplectic twist maps. Zbl 1290.37024
Arnaud, M.-C.
2014
When are the invariant submanifolds of symplectic dynamics Lagrangian? Zbl 1308.37026
Arnaud, Marie-Claude
2014
Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting. Zbl 1269.37032
Arnaud, M.-C.
2013
$$C^1$$-generic billiard tables have a dense set of periodic points. Zbl 1417.37094
Arnaud, Marie-Claude
2013
Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures. Zbl 1269.37031
Arnaud, M.-C.
2012
The link between the shape of the irrational Aubry-Mather sets and their Lyapunov exponents. Zbl 1257.37028
Arnaud, Marie-Claude
2011
A nondifferentiable essential irrational invariant curve for a $$C^1$$ symplectic twist map. Zbl 1276.37034
Arnaud, Marie-Claude
2011
Pseudographs and the Lax-Oleinik semi-group: a geometric and dynamical interpretation. Zbl 1284.05120
Arnaud, M-C
2011
Green bundles and related topics. Zbl 1243.37037
Arnaud, Marie-Claude
2011
A particular minimization property implies $$C^{0}$$-integrability. Zbl 1214.37044
Arnaud, M.-C.
2011
On a theorem due to Birkhoff. Zbl 1216.37020
Arnaud, Marie-Claude
2010
Three results on the regularity of the curves that are invariant by an exact symplectic twist map. Zbl 1177.53070
Arnaud, M.-C.
2009
Green bundles and regularity of $$C^0$$-Lagrangians invariant graphs of Tonelli flows. Zbl 1143.70009
Arnaud, Marie-Claude
2008
The tiered Aubry set for autonomous Lagrangian functions. Zbl 1152.37025
Arnaud, Marie-Claude
2008
Hyperbolic periodic orbits and Mather sets in certain symmetric cases. Zbl 1118.37030
Arnaud, M.-C.
2006
Generic symplectic dynamics. Zbl 1084.37017
Arnaud, Marie-Claude; Bonatti, Christian; Crovisier, Sylvain
2005
Convergence of the semi-group of Lax-Oleinik: a geometric point of view. Zbl 1181.37018
Arnaud, M. C.
2005
Approximation des ensembles $$\omega$$-limites des difféomorphismes par des orbites pério-diques. (Approximation of $$\omega$$-limit sets of diffeomorphisms by periodic orbits). Zbl 1024.37011
Arnaud, Marie-Claude
2003
The generic symplectic $$C^1$$-diffeomorphisms of four-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely elliptic periodic point. Zbl 1030.37037
Arnaud, Marie-Claude
2002
Creation of connections in $$C^1$$-topology. Zbl 0997.37007
Arnaud, Marie-Claude
2001
Symplectic $$C^1$$-diffeomorphisms of 4-dimensional manifolds. Zbl 0964.37034
Arnaud, Marie-Claude
2000
Existence of completely elliptic periodic orbits of symmetric and convex Hamiltonians. Zbl 0943.37029
Arnaud, Marie-Claude
1999
The $$C^1$$ closing lemma. Zbl 0920.58039
Arnaud, Marie-Claude
1998
On the type of certain periodic orbits minimizing the Lagrangian action. Zbl 0901.58013
Arnaud, Marie-Claude
1998
An “orbit closing lemma”. Zbl 0867.58040
Arnaud, Marie-Claude
1996
Creation of periodic points of all types in the neighbourhood of K.A.M. tori. Zbl 0853.58046
Arnaud, Marie-Claude
1995
Type of critical points of Hamiltonian functions and of fixed points of symplectic diffeomorphisms. Zbl 0811.58022
Arnaud, Marie-Claude
1994
Types of fixed points of symplectic diffeomorphisms on $$\mathbb{T}^ n\times \mathbb{R}^ n$$. Zbl 0758.58009
Arnaud, Marie-Claude
1992
Sur les points fixes des difféomorphismes exacts symplectiques de $$T^ n\times R^ n$$. (Fixed points of exact symplectic diffeomorphisms of $$T^ n\times R^ n)$$. Zbl 0696.57017
Arnaud, Marie-Claude
1989
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#### Cited by 120 Authors

 16 Arnaud, Marie-Claude 6 Crovisier, Sylvain 4 Bessa, Mário 3 Bochi, Jairo 3 Bonatti, Christian 3 Le Calvez, Patrice 3 Qin, Wenxin 3 Wang, Kaizhi 3 Wang, Yanan 3 Yan, Jun 2 Abdenur, Flavio 2 Arbieto, Alexander 2 Arcostanzo, Marc 2 Avila Cordeiro de Melo, Artur 2 Berger, Pierre 2 Bernard, Patrick 2 Bolle, Philippe 2 Catalan, Thiago 2 Contreras, Gonzalo 2 Figalli, Alessio 2 Gorodetski, Anton 2 Kaloshin, Vadim Yu. 2 Lopes Dias, João 2 Oliveira Dos Santos, Joana 2 Rifford, Ludovic 2 Sorrentino, Alfonso 2 Tahzibi, Ali 2 Turaev, Dmitry V. 2 Visscher, Daniel A. 2 Wang, Xiaodong 1 Abbondandolo, Alberto 1 Abreu, Miguel 1 Alishah, Hassan Najafi 1 Amorim, Lino 1 Anosov, Dmitriĭ Viktorovich 1 Azevedo, Assis 1 Azevedo, Davide 1 Bahabadi, Alireza Zamani 1 Bernardi, Olga 1 Berti, Massimiliano 1 Bialy, Misha 1 Butler, Leo T. 1 Buzzi, Jérôme 1 Cardin, Franco 1 Dias Carneiro, Mario Jorge 1 Duarte, Pedro 1 Ferreira, Célia 1 Fisher, Todd L. 1 Florio, Anna 1 Gan, Shaobo 1 Garcia, Fortino 1 Ginzburg, Viktor L’vovich 1 Gourmelon, Nicolas 1 Guihéneuf, Pierre-Antoine 1 Gürel, Basak Zehra 1 Horita, Vanderlei 1 Huang, Guan 1 Katić, Jelena 1 Khanin, Konstantin M. 1 Klempnauer, Stefan 1 Koropecki, Andres 1 Kovaleva, A. M. 1 Labrousse, Clémence 1 Lee, Manseob 1 Leguil, Martin 1 Li, Xinxiang 1 Li, Yong 1 Liu, Qihuai 1 Lomelí, Héctor E. 1 Lopes, Artur Oscar 1 Louati, Hanen 1 Macarini, Leonardo 1 Marco, Jean-Pierre 1 Margaliot, Michael 1 Markarian, Roberto 1 Meiss, James D. 1 Melguizo Padial, M. A. 1 Mengue, Jairo K. 1 Milinković, Darko 1 Nassiri, Meysam 1 Nikolić, Jovana 1 Obata, Davi 1 Oh, Yong-Geun 1 Oliffson Kamphorst, Sylvie 1 Passeggi, Alejandro 1 Pinto de Carvalho, Sônia 1 Polterovich, Leonid Viktorovich 1 Potrie, Rafael 1 Rapoport, Anna 1 Ribeiro, Raquel 1 Ríos-Zertuche, Rodolfo 1 Roberts, Gareth E. 1 Rocha, Alexandre 1 Rocha, Jorge 1 Rodriguez-Hertz, Federico 1 Rodriguez Hertz, Jana 1 Rom-Kedar, Vered 1 Roos, Valentine 1 Rouleux, Michel 1 Saghin, Radu ...and 20 more Authors
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#### Cited in 52 Serials

 10 Ergodic Theory and Dynamical Systems 6 Communications in Mathematical Physics 5 Discrete and Continuous Dynamical Systems 4 Journal of Differential Equations 4 Mathematische Zeitschrift 4 Proceedings of the American Mathematical Society 3 Nonlinearity 3 Transactions of the American Mathematical Society 3 Annals of Mathematics. Second Series 3 Dynamical Systems 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Chaos, Solitons and Fractals 2 Advances in Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Duke Mathematical Journal 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Mémoires de la Société Mathématique de France. Nouvelle Série 2 Journal of Dynamics and Differential Equations 2 Calculus of Variations and Partial Differential Equations 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of the Institute of Mathematics of Jussieu 2 Science China. Mathematics 1 Communications on Pure and Applied Mathematics 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Mathematical Notes 1 Journal of Geometry and Physics 1 Annales de l’Institut Fourier 1 Automatica 1 Bulletin de la Société Mathématique de France 1 Geometriae Dedicata 1 Publications Mathématiques 1 Inventiones Mathematicae 1 Mathematische Annalen 1 Physica D 1 Revista Matemática Iberoamericana 1 L’Enseignement Mathématique. 2e Série 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Selecta Mathematica. New Series 1 Abstract and Applied Analysis 1 Geometry & Topology 1 Regular and Chaotic Dynamics 1 Communications in Nonlinear Science and Numerical Simulation 1 Communications in Contemporary Mathematics 1 Differential Equations 1 Advanced Nonlinear Studies 1 Theoretical and Applied Mechanics 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Geometric Mechanics 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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#### Cited in 17 Fields

 89 Dynamical systems and ergodic theory (37-XX) 17 Differential geometry (53-XX) 12 Mechanics of particles and systems (70-XX) 5 Partial differential equations (35-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Ordinary differential equations (34-XX) 3 Manifolds and cell complexes (57-XX) 2 Measure and integration (28-XX) 2 General topology (54-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Real functions (26-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

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