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Building Anosov flows on $3$–manifolds

François Béguin , Christian Bonatti , Bin Yu
Geometry and Topology, 2017, 21 (3), pp.1837 - 1930. ⟨10.2140/gt.2017.21.1837⟩
Article dans une revue hal-01565095v1

Robust criterion for the existence of nonhyperbolic ergodic measures

Jairo Bochi , Christian Bonatti , Lorenzo J. Díaz
Communications in Mathematical Physics, 2016, 344 (3), pp. 751-795 ⟨10.1007/s00220-016-2644-5⟩
Article dans une revue hal-01407967v1

Robust existence of nonhyperbolic ergodic measures with positive entropy and full support

Christian Bonatti , Lorenzo J. Díaz , Dominik Kwietniak
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2021, 22 (4), pp.1643-1672. ⟨10.2422/2036-2145.202001_014⟩
Article dans une revue hal-03865192v1
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Dynamiques symplectiques génériques

Marie-Claude Arnaud , Christian Bonatti , Sylvain Crovisier
Ergodic Theory and Dynamical Systems, 2005, 25 (5), pp.1401-1436. ⟨10.1017/S0143385704000975⟩
Article dans une revue hal-00538131v1
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Local density of diffeomorphisms with large centralizers

Christian Bonatti , Sylvain Crovisier , Gioia Vago , Amie Wilkinson
2007
Pré-publication, Document de travail hal-00175146v1
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Nonuniform hyperbolicity for C^1-generic diffeomorphisms

Flavio Abdenur , Christian Bonatti , Sylvain Crovisier
2008
Pré-publication, Document de travail hal-00322876v1

Foliated hyperbolicity and foliations with hyperbolic leaves

Christian Bonatti , Xavier Gómez-Mont , Matilde Martínez
Ergodic Theory and Dynamical Systems, 2020, 40 (4), pp.881-903. ⟨10.1017/etds.2018.61⟩
Article dans une revue hal-01996909v1

Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics

Doris Bohnet , Christian Bonatti
Ergodic Theory and Dynamical Systems, 2016, 36 (4), pp.1067-1105 ⟨10.1017/etds.2014.102⟩
Article dans une revue hal-01410903v1

A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class

Christian Bonatti , Katsutoshi Shinohara
2022
Pré-publication, Document de travail hal-03793065v1

Anomalous partially hyperbolic diffeomorphisms III: Abundance and incoherence

Christian Bonatti , Andrey Gogolev , Andy Hammerlindl , Rafael Potrie
Geometry and Topology, 2020, 24 (4), pp.1751-1790. ⟨10.2140/gt.2020.24.1751⟩
Article dans une revue hal-03043879v1
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Small C1 actions of semidirect products on compact manifolds

Christian Bonatti , Sang-Hyun Kim , Thomas Koberda , Michele Triestino
Algebraic and Geometric Topology, 2020, 20 (6), pp.3183-3203. ⟨10.2140/agt.2020.20.3183⟩
Article dans une revue hal-02314202v1

A $C^1$ Anosov diffeomorphism with a horseshoe that attracts almost any point

Christian Bonatti , S. S. Minkov , A. V. Okunev , I. S. Shilin
Functional Analysis and Its Applications, 2017, 51 (2), pp.144 - 147. ⟨10.1007/s10688-017-0176-1⟩
Article dans une revue hal-01556479v1

Lorenz attractors and the modular surface*

C. Bonatti , Tali Pinsky
Nonlinearity, 2021, 34 (6), pp.4315-4331. ⟨10.1088/1361-6544/abf8fa⟩
Article dans une revue hal-03404498v1
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Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan

Christian Bonatti , Boris Kolev
Ergodic Theory and Dynamical Systems, 1992, 12 (4), pp.677-682
Article dans une revue hal-00003268v1

What is... a Blender?

Christian Bonatti , Sylvain Crovisier , Lorenzo J. Díaz , Amie Wilkinson
Notices of the American Mathematical Society, 2016, 63 (10), pp.1175 - 1178. ⟨10.1090/noti1438⟩
Article dans une revue hal-01616140v1

Existence of common zeros for commuting vector fields on 3‐manifolds II. Solving global difficulties

Sébastien Alvarez , Christian Bonatti , Bruno Santiago
Proceedings of the London Mathematical Society, 2020, 121 (4), pp.828-875. ⟨10.1112/plms.12342⟩
Article dans une revue hal-03036013v1

Topological classification of Morse–Smale diffeomorphisms on 3-manifolds

Christian Bonatti , V. Grines , O. Pochinka
Duke Mathematical Journal, 2019, 168 (13), pp.2507-2558. ⟨10.1215/00127094-2019-0019⟩
Article dans une revue hal-02468888v1

Transverse foliations on the torus $\mathbb T^2$ and partially hyperbolic diffeomorphisms on 3-manifolds

Christian Bonatti , Jinhua Zhang
Commentarii Mathematici Helvetici, 2017, 92 (3), pp.513 - 550. ⟨10.4171/CMH/418⟩
Article dans une revue hal-01591646v1

Connectedness of the space of smooth actions of $\mathbb{Z}^n$ on the interval

Christian Bonatti , Hélène Eynard-Bontemps
Ergodic Theory and Dynamical Systems, 2016, 36 (07), pp.2076 - 2106. ⟨10.1017/etds.2015.3⟩
Article dans une revue hal-01414874v1

A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class

C. Bonatti , Katsutoshi Shinohara
Ergodic Theory and Dynamical Systems, 2023, pp.1-63. ⟨10.1017/etds.2023.76⟩
Article dans une revue hal-04362255v1

Volume hyperbolicity and wildness

Christian Bonatti , Katsutoshi Shinohara
Ergodic Theory and Dynamical Systems, 2018, 38 (3), pp.886-920. ⟨10.1017/etds.2016.51⟩
Article dans une revue hal-01801537v1

Surface homeomorphisms with zero dimensional singular set

Boris Kolev , Christian Bonatti
Topology and its Applications, 1998, 90, pp.69-95. ⟨10.1016/S0166-8641(97)00179-X⟩
Article dans une revue hal-00003264v1
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Recurrence and genericity

Christian Bonatti , Sylvain Crovisier
2003
Pré-publication, Document de travail hal-00000449v1
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The C1 generic diffeomorphism has trivial centralizer

Christian Bonatti , Sylvain Crovisier , Amie Wilkinson
2008
Pré-publication, Document de travail hal-00271388v1

The centralizer of a C1 generic diffeomorphism is trivial

Christian Bonatti , Sylvain Crovisier , Amie Wilkinson
2007
Pré-publication, Document de travail hal-00150944v1

Anosov diffeomorphism with a horseshoe that attracts almost any point

Christian Bonatti , Stanislav Minkov , Alexey Okunev , Ivan Shilin
Discrete and Continuous Dynamical Systems - Series A, 2020, 40 (1), pp.441-465. ⟨10.3934/dcds.2020017⟩
Article dans une revue hal-02524815v1
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Minimal number of periodic orbits for nonsingular Morse-Smale flows in odd dimension

M. A. Bertolim , C. Bonatti , M. P. Mello , G. M. Vago
2023
Pré-publication, Document de travail hal-02946281v2

A criterion for zero averages and full support of ergodic measures

Christian Bonatti , Lorenzo J. Díaz , Jairo Bochi
Moscow Mathematical Journal, 2018, 18 (1), pp.15-61
Article dans une revue hal-01758598v1

Realization of Morse–Smale diffeomorphisms on 3-manifolds

Christian Bonatti , V. Z. Grines , Olga Pochinka
Proceedings of the Steklov Institute of Mathematics, 2017, 297 (1), pp.35 - 49. ⟨10.1134/S0081543817040034⟩
Article dans une revue hal-01613096v1

Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples

Christian Bonatti , Andrey Gogolev , Rafael Potrie
Inventiones Mathematicae, 2016, 206 (3), pp.801 - 836. ⟨10.1007/s00222-016-0663-7⟩
Article dans une revue hal-01446863v1