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Bonatti, Christian

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Author ID: bonatti.christian Recent zbMATH articles by "Bonatti, Christian"
Published as: Bonatti, C.; Bonatti, Ch.; Bonatti, Christian
Homepage: http://bonatti.perso.math.cnrs.fr/
External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
Documents Indexed: 130 Publications since 1985, including 3 Books
all top 5

Co-Authors

11 single-authored
24 Díaz, Lorenzo Justiniano
16 Crovisier, Sylvain
15 Grines, Vyacheslav Zigmundovich
9 Viana, Marcelo
8 Pochinka, Olga Vital’evna
7 Wilkinson, Amie
6 Potrie, Rafael
5 Abdenur, Flavio
5 Bochi, Jairo
5 Gómez-Mont, Xavier
5 Medvedev, Vladislav Sergeevich
5 Pécou, Elisabeth
4 Béguin, François
4 Langevin, Rémi
4 Yang, Dawei
4 Zhang, Jinhua
3 Gan, Shaobo
3 Gourmelon, Nicolas
3 Guelman, Nancy
3 Shinohara, Katsutoshi
2 Gogolev, Andrey
2 Haefliger, André
2 Hattab, Hawete
2 Kolev, Boris
2 Li, Ming
2 Minkov, Stanislav S.
2 Pujals, Enrique Ramiro
2 Pumariño, Antonio
2 Salhi, Ezzeddine
2 Santiago, Bruno
2 Vago, Gioia Maria
2 Wen, Lan
1 Alvarez, Sébastien
1 Alves, José Ferreira
1 Arnaud, Marie-Claude
1 Baladi, Viviane
1 Baraviera, Alexandre Tavares
1 Bohnet, Doris
1 Bowden, Jonathan Peter
1 Da Luz, Adriana
1 Dolecki, Szymon
1 Dufraine, Emmanuel
1 Eynard-Bontemps, Hélène
1 Farinelli, Églantine
1 Firmo, Sebastião
1 Fisher, Todd L.
1 Franks, John M.
1 Gambaudo, Jean-Marc
1 Gelfert, Katrin Grit
1 Gorodetski, Anton
1 Hammerlindl, Andy
1 Kiriki, Shin
1 Laudenbach, François
1 Lion, Jean-Marie
1 Lodha, Yash
1 Martínez, Matilde
1 Matheus, Carlos
1 Monteverde, Ignacio
1 Moussu, Robert
1 Navas, Andrés
1 Nogura, Tsugunori
1 Okunev, A. V.
1 Okunev, Alexey
1 Paoluzzi, Luisa
1 Paris, Luis
1 Parwani, Kamlesh
1 Rivas, Cristóbal
1 Rocha, Jorge
1 Schmitt, Bernard
1 Shilin, I. S.
1 Shilin, Ivan
1 Teixeira, Marco Antonto
1 Tresser, Charles
1 Triestino, Michele
1 Turcat, Gaël
1 Ures, Raúl
1 Vietez, J. L.
1 Vila Freyer, Ricardo Francisco
1 Villadelprat, Jordi
1 Vivier, Thérèse
1 Vuillemin, F.
1 Yu, Bin
1 Yu, Boming
all top 5

Serials

22 Ergodic Theory and Dynamical Systems
7 Topology
5 Topology and its Applications
4 Israel Journal of Mathematics
4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
4 Transactions of the American Mathematical Society
4 Journal of the Institute of Mathematics of Jussieu
3 Nonlinearity
3 Commentarii Mathematici Helvetici
3 Fundamenta Mathematicae
3 Publications Mathématiques
3 Inventiones Mathematicae
3 Mathematische Zeitschrift
3 Proceedings of the London Mathematical Society. Third Series
3 Comptes Rendus de l’Académie des Sciences. Série I
3 Discrete and Continuous Dynamical Systems
3 Geometry & Topology
3 Annals of Mathematics. Second Series
3 Journal of Modern Dynamics
2 Journal of Differential Equations
2 Proceedings of the American Mathematical Society
2 Boletim da Sociedade Brasileira de Matemática. Nova Série
2 Doklady Mathematics
2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
2 Proceedings of the Steklov Institute of Mathematics
1 Communications in Mathematical Physics
1 Annales de l’Institut Fourier
1 Duke Mathematical Journal
1 Functional Analysis and its Applications
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Notices of the American Mathematical Society
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Journal of Mathematical Sciences (New York)
1 Computational and Applied Mathematics
1 Journal of Dynamical and Control Systems
1 Moscow Mathematical Journal
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
1 Astérisque
1 Ensaios Matemáticos
1 Groups, Geometry, and Dynamics
1 Electronic Research Announcements in Mathematical Sciences
1 Science China. Mathematics

Publications by Year

Citations contained in zbMATH

117 Publications have been cited 1,772 times in 835 Documents Cited by Year
Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective. Zbl 1060.37020
Bonatti, Christian; Díaz, Lorenzo J.; Viana, Marcelo
200
2005
SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Zbl 0962.37012
Alves, José F.; Bonatti, Christian; Viana, Marcelo
129
2000
A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources. Zbl 1049.37011
Bonatti, C.; Díaz, L. J.; Pujals, E. R.
110
2003
Recurrence and genericity. Zbl 1071.37015
Bonatti, Christian; Crovisier, Sylvain
105
2004
SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Zbl 0996.37033
Bonatti, Christian; Viana, Marcelo
104
2000
Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms. Zbl 1246.37040
Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain
62
2011
Persistent nonhyperbolic transitive diffeomorphisms. Zbl 0852.58066
Bonatti, Christian; Díaz, Lorenzo J.
61
1996
Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\). Zbl 0959.37017
Bonatti, C.; Grines, V.
41
2000
Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices. (Genericity of non-zero Lyapunov exponents for deterministic products of matrices). Zbl 1025.37018
Bonatti, Christian; Gómez-Mont, Xavier; Viana, Marcelo
38
2003
Perturbations of the derivative along periodic orbits. Zbl 1175.37027
Bonatti, Christian; Gourmelon, Nikolas; Vivier, Thérèse
36
2006
Robust heterodimensional cycles and \(C^1\)-generic dynamics. Zbl 1156.37004
Bonatti, Christian; Díaz, Lorenzo J.
33
2008
Periodic points and homoclinic classes. Zbl 1144.37007
Abdenur, F.; Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wen, L.
31
2007
Removing zero Lyapunov exponents. Zbl 1048.37026
Baraviera, Alexandre T.; Bonatti, Christian
29
2003
Transitive partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1074.57015
Bonatti, Christian; Wilkinson, Amie
27
2005
Lorenz attractors with arbitrary expanding dimension. Zbl 0896.58043
Bonatti, Christian; Pumariño, António; Viana, Marcelo
24
1997
Lyapunov exponents with multiplicity 1 for deterministic products of matrices. Zbl 1087.37017
Bonatti, C.; Viana, M.
22
2004
On maximal transitive sets of generic diffeomorphisms. Zbl 1032.37011
Bonatti, Christian; Dıaz, Lorenzo J.
21
2002
Topological classification of gradient-like diffeomorphisms on 3-manifolds. Zbl 1056.37023
Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E.
20
2004
Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves. Zbl 1157.37309
Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E.
20
2002
There is no “Shadowing lemma” for partially hyperbolic dynamics. Zbl 0973.37016
Bonatti, Christian; Díaz, Lorenzo J.; Turcat, Gaël
20
2000
Abundance of \(C^{1}\)-robust homoclinic tangencies. Zbl 1300.37013
Bonatti, Christian; Díaz, Lorenzo J.
19
2012
Towards a global view of dynamical systems, for the \(C^{1}\)-topology. Zbl 1256.37006
Bonatti, C.
19
2011
Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms. Zbl 1031.37030
Bonatti, Christian; Díaz, Lorenzo J.; Ures, Raúl
18
2002
Robust criterion for the existence of nonhyperbolic ergodic measures. Zbl 1368.37036
Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J.
17
2016
Classification of Morse-Smale diffeomorphisms with a finite set of heteroclinic orbits on 3-manifolds. Zbl 1138.37307
Bonatti, C.; Grines, V. Z.; Pochinka, O. V.
17
2005
Non-hyperbolic ergodic measures with large support. Zbl 1195.37013
Bonatti, Christian; Díaz, Lorenzo J.; Gorodetski, Anton
16
2010
Robustly transitive sets and heterodimensional cycles. Zbl 1056.37024
Bonatti, Christian; Díaz, Lorenzo J.; Pujals, Enrique R.; Rocha, Jorge
16
2003
An example of transitive Anosov flows transversal to a torus and not conjugated to a suspension. Zbl 0826.58026
Bonatti, Christian; Langevin, Remi
16
1994
Statistical behaviour of the leaves of certain holomorphic foliations. Zbl 1010.37025
Bonatti, Christian; Gómez-Mont, Xavier
15
2001
Smale diffeomorphisms of surfaces. With the collab. of Emmanuelle Jeandenans. Zbl 0922.58058
Bonatti, C.; Langevin, R.
15
1998
Un point fixe commun pour des difféomorphismes commutants de \(S^ 2\). (A common fixed point for commutating diffeomorphisms of \(S^ 2\).). Zbl 0689.57019
Bonatti, Christian
15
1989
Stabilization of heterodimensional cycles. Zbl 1284.37020
Bonatti, C.; Díaz, L. J.; Kiriki, S.
14
2012
Generic symplectic dynamics. Zbl 1084.37017
Arnaud, Marie-Claude; Bonatti, Christian; Crovisier, Sylvain
14
2005
Non-wandering sets with non-empty interiors. Zbl 1083.37020
Abdenur, Flavio; Bonatti, Christian; Díaz, Lorenzo J.
14
2004
Heteroclinic connections and genericity of infinitely many sinks and sources. Zbl 0944.37012
Bonatti, Christian; Díaz, Lorenzo
14
1999
Perturbation of the Lyapunov spectra of periodic orbits. Zbl 1268.37027
Bochi, J.; Bonatti, C.
12
2012
The \(C^1\) generic diffeomorphism has trivial centralizer. Zbl 1177.37025
Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie
12
2009
On the existence of non-trivial homoclinic classes. Zbl 1128.37021
Bonatti, Christian; Gan, Shaobo; Wen, Lan
11
2007
Generic diffeomorphisms on compact surfaces. Zbl 1089.37032
Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain; Díaz, Lorenzo J.
11
2005
Difféomorphismes commutants des surfaces et stabilité des fibrations en tores. (Commuting diffeomorphisms of surfaces and stability of fibrations by tori). Zbl 0703.57015
Bonatti, Christian
11
1990
Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics. Zbl 1362.37075
Bohnet, Doris; Bonatti, Christian
10
2016
The \(C^{1+\alpha}\) hypothesis in Pesin theory revisited. Zbl 1312.37018
Bonatti, Christian; Crovisier, Sylvain; Shinohara, Katsutoshi
10
2013
Local density of diffeomorphisms with large centralizers. Zbl 1163.58003
Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie
10
2008
Smale flows in dimension 3: finite presentations of invariant neighbourhoods of saddle sets. Zbl 1102.37307
Béguin, F.; Bonatti, C.
10
2002
Foliations in \(\mathbb{C} P(n)\): About hyperbolic holonomy for minimal exceptional sets. Zbl 0782.32023
Bonatti, C.; Langevin, R.; Moussu, R.
10
1992
Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication. Zbl 1303.37008
Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Gourmelon, N.
9
2013
Statistical behaviour of the leaves of Riccati foliations. Zbl 1209.37055
Bonatti, Ch.; Gómez-Mont, X.; Vila-Freyer, R.
9
2010
On the hyperbolicity of homoclinic classes. Zbl 1200.37023
Bonatti, Christian; Gan, Shaobo; Yang, Dawei
9
2009
Abnormal escape rates from nonuniformly hyperbolic sets. Zbl 0987.37018
Baladi, Viviane; Bonatti, Christian; Schmitt, Bernard
9
1999
Rigidity for \(C^1\) actions on the interval arising from hyperbolicity. I: Solvable groups. Zbl 1433.37030
Bonatti, C.; Monteverde, Ignacio; Navas, Andres; Rivas, Cristobal
8
2017
Robust vanishing of all Lyapunov exponents for iterated function systems. Zbl 1284.37044
Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J.
8
2014
Commuting analytic vector fields in dimension 3 or 4: Existence of common zeros. Zbl 0776.57013
Bonatti, Christian
8
1992
Center manifolds for partially hyperbolic sets without strong unstable connections. Zbl 1362.37069
Bonatti, Christian; Crovisier, Sylvain
7
2016
What is \(\ldots a\) blender? Zbl 1352.37075
Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wilkinson, A.
7
2016
Anomalous partially hyperbolic diffeomorphisms. II: Stably ergodic examples. Zbl 1370.37069
Bonatti, Christian; Gogolev, Andrey; Potrie, Rafael
7
2016
Dominated Pesin theory: convex sum of hyperbolic measures. Zbl 1408.37054
Bochi, Jairo; Bonatti, Christian; Gelfert, Katrin
6
2018
Axiom A diffeomorphisms derived from Anosov flows. Zbl 1201.37033
Bonatti, Christian; Guelman, Nancy
6
2010
\(C^1\)-generic conservative diffeomorphisms have trivial centralizer. Zbl 1149.37017
Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie
6
2008
Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices. Zbl 1153.37340
Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pochinka, O. V.
6
2007
Classification of Morse-Smale diffeomorphisms with the chain of saddles on 3-manifolds. Zbl 1222.37021
Bonatti, Christian; Grines, Viacheslav; Pochinka, Olga
6
2006
Abundance of stable ergodicity. Zbl 1052.37023
Bonatti, Christian; Matheus, Carlos; Viana, Marcelo; Wilkinson, Amie
6
2004
On Morse-Smale diffeomorphisms without heteroclinic intersections on three-manifolds. Zbl 1011.37013
Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pécou, E.
6
2002
Two-dimensional links and diffeomorphisms on 3-manifolds. Zbl 1008.37013
Bonatti, Christian; Grines, Viatcheslav; Pécou, Elisabeth
6
2002
On the topological classification of gradient-like diffeomorphisms without heteroclinic curves on three-dimensional manifolds. Zbl 1041.37007
Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pecou, E.
6
2001
Compact leaves of a generic codimension 1 foliation. Zbl 0828.57022
Bonatti, Christian; Firmo, Sebastião
6
1994
Foliations near to a fibration. Zbl 1214.53022
Bonatti, C.
6
1993
Déformations de feuilletages. (Deformations of foliations). Zbl 0703.57013
Bonatti, C.; Haefliger, A.
6
1990
Building Anosov flows on 3-manifolds. Zbl 1375.37083
Béguin, François; Bonatti, Christian; Yu, Bin
5
2017
Anomalous partially hyperbolic diffeomorphisms. I: Dynamically coherent examples. Zbl 1375.37093
Bonatti, Christian; Parwani, Kamlesh; Potrie, Rafael
5
2016
Dominated chain recurrent class with singularities. Zbl 1371.37027
Bonatti, Christian; Gan, Shaobo; Yang, Dawei
5
2015
A robustly chain transitive attractor with singularities of different indices. Zbl 1304.37002
Bonatti, Christian; Li, Ming; Yang, Dawei
5
2013
On the existence of attractors. Zbl 1272.37019
Bonatti, Christian; Li, Ming; Yang, Dawei
5
2013
Roots in the mapping class groups. Zbl 1160.57014
Bonatti, Christian; Paris, Luis
5
2009
3-manifolds which are orbit spaces of diffeomorphisms. Zbl 1165.37001
Bonatti, C.; Paoluzzi, L.
5
2008
Global dominated splittings and the \( C^1\) Newhouse phenomenon. Zbl 1088.37013
Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain
5
2006
Topological equivalence of saddle connections in dimension 3. Zbl 1056.37030
Bonatti, Christian; Dufraine, Emmanuel
5
2003
Discontinuity of the Hausdorff dimension of hyperbolic sets. Zbl 0852.54038
Bonatti, Christian; Díaz, Lorenzo Justiniano; Viana, Marcelo
5
1995
Wandering domains for infinitely renormalizable diffeomorphisms of the disk. Zbl 0843.57016
Bonatti, Christian; Gambaudo, Jean Marc; Lion, Jean Marie; Tresser, Charles
5
1994
The index of holomorphic vector fields on singular varieties. I. Zbl 0810.32017
Bonatti, Ch.; Gómez-Mont, X.
5
1994
Quasi-orbit spaces associated to \(T_0\)-spaces. Zbl 1218.54025
Bonatti, C.; Hattab, H.; Salhi, E.
4
2011
Super exponential growth of the number of periodic orbits inside homoclinic classes. Zbl 1145.37015
Bonatti, Christian; Díaz, Lorenzo J.; Fisher, Todd
4
2008
The index of stable critical points. Zbl 1013.37016
Bonatti, Christian; Villadelprat, Jordi
4
2002
Dynamical systems in dimension 2 and 3: conjugacy invariants and classification. Zbl 1121.37306
Bonatti, C.; Grines, V.; Langevin, R.
4
2001
Hyperbolicity as an obstruction to smoothability for one-dimensional actions. Zbl 1428.37029
Bonatti, Christian; Lodha, Yash; Triestino, Michele
3
2019
Realization of Morse-Smale diffeomorphisms on 3-manifolds. Zbl 1377.37044
Bonatti, Ch.; Grines, V. Z.; Pochinka, Olga V.
3
2017
Transverse foliations on the torus \(\mathbb{T}^2\) and partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1380.37065
Bonatti, Christian; Zhang, Jinhua
3
2017
Hasse diagrams and orbit class spaces. Zbl 1213.54050
Bonatti, C.; Hattab, H.; Salhi, E.; Vago, G.
3
2011
Transitive Anosov flows and Axiom-A diffeomorphisms. Zbl 1173.37028
Bonatti, Christian; Guelman, Nancy
3
2009
A Hölder continuous vector field tangent to many foliations. Zbl 1147.37313
Bonatti, Christian; Franks, John
3
2004
Recurrence and genericity. Zbl 1027.37011
Bonatti, Christian; Crovisier, Sylvain
3
2003
Surface homeomorphisms with zero-dimensional singular set. Zbl 0929.37013
Bonatti, C.; Kolev, B.
3
1998
Cubic tangencies and hyperbolic diffeomorphisms. Zbl 0943.37012
Bonatti, Ch.; Díaz, L. J.; Vuillemin, F.
3
1998
Topological classification of Morse-Smale diffeomorphisms on \(3\)-manifolds. Zbl 1435.37050
Bonatti, C.; Grines, V.; Pochinka, O.
2
2019
Periodic measures and partially hyperbolic homoclinic classes. Zbl 1421.37018
Bonatti, Christian; Zhang, Jinhua
2
2019
A criterion for zero averages and full support of ergodic measures. Zbl 07069469
Bonatti, Christian; Díaz, Lorenzo J.; Bochi, Jairo
2
2018
Weak hyperbolic structures and robust properties of diffeomorphisms and flows. Zbl 1401.37037
Bonatti, Christian; da Luz, Adriana
2
2018
Many intermingled basins in dimension 3. Zbl 1398.37017
Bonatti, Christian; Potrie, Rafael
2
2018
Centralizers of \(C^1\)-contractions of the half line. Zbl 1326.22019
Bonatti, Christian; Farinelli, Églantine
2
2015
Flexible periodic points. Zbl 1352.37076
Bonatti, Christian; Shinohara, Katsutoshi
2
2015
Smooth conjugacy classes of circle diffeomorphisms with irrational rotation number. Zbl 1346.37045
Bonatti, Christian; Guelman, Nancy
2
2014
Hyperbolicity as an obstruction to smoothability for one-dimensional actions. Zbl 1428.37029
Bonatti, Christian; Lodha, Yash; Triestino, Michele
3
2019
Topological classification of Morse-Smale diffeomorphisms on \(3\)-manifolds. Zbl 1435.37050
Bonatti, C.; Grines, V.; Pochinka, O.
2
2019
Periodic measures and partially hyperbolic homoclinic classes. Zbl 1421.37018
Bonatti, Christian; Zhang, Jinhua
2
2019
Topological classification of Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds. Zbl 1431.37032
Bonatti, Ch.; Grines, V.; Laudenbach, F.; Pochinka, O.
1
2019
Dominated Pesin theory: convex sum of hyperbolic measures. Zbl 1408.37054
Bochi, Jairo; Bonatti, Christian; Gelfert, Katrin
6
2018
A criterion for zero averages and full support of ergodic measures. Zbl 07069469
Bonatti, Christian; Díaz, Lorenzo J.; Bochi, Jairo
2
2018
Weak hyperbolic structures and robust properties of diffeomorphisms and flows. Zbl 1401.37037
Bonatti, Christian; da Luz, Adriana
2
2018
Many intermingled basins in dimension 3. Zbl 1398.37017
Bonatti, Christian; Potrie, Rafael
2
2018
Volume hyperbolicity and wildness. Zbl 1390.37049
Bonatti, Christian; Shinohara, Katsutoshi
1
2018
Rigidity for \(C^1\) actions on the interval arising from hyperbolicity. I: Solvable groups. Zbl 1433.37030
Bonatti, C.; Monteverde, Ignacio; Navas, Andres; Rivas, Cristobal
8
2017
Building Anosov flows on 3-manifolds. Zbl 1375.37083
Béguin, François; Bonatti, Christian; Yu, Bin
5
2017
Realization of Morse-Smale diffeomorphisms on 3-manifolds. Zbl 1377.37044
Bonatti, Ch.; Grines, V. Z.; Pochinka, Olga V.
3
2017
Transverse foliations on the torus \(\mathbb{T}^2\) and partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1380.37065
Bonatti, Christian; Zhang, Jinhua
3
2017
Existence of common zeros for commuting vector fields on three manifolds. Zbl 1405.37026
Bonatti, Christian; Santiago, Bruno
1
2017
A \(C^1\) Anosov diffeomorphism with a horseshoe that attracts almost any point. Zbl 1377.37047
Bonatti, C.; Minkov, S. S.; Okunev, A. V.; Shilin, I. S.
1
2017
Robust criterion for the existence of nonhyperbolic ergodic measures. Zbl 1368.37036
Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J.
17
2016
Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics. Zbl 1362.37075
Bohnet, Doris; Bonatti, Christian
10
2016
Center manifolds for partially hyperbolic sets without strong unstable connections. Zbl 1362.37069
Bonatti, Christian; Crovisier, Sylvain
7
2016
What is \(\ldots a\) blender? Zbl 1352.37075
Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wilkinson, A.
7
2016
Anomalous partially hyperbolic diffeomorphisms. II: Stably ergodic examples. Zbl 1370.37069
Bonatti, Christian; Gogolev, Andrey; Potrie, Rafael
7
2016
Anomalous partially hyperbolic diffeomorphisms. I: Dynamically coherent examples. Zbl 1375.37093
Bonatti, Christian; Parwani, Kamlesh; Potrie, Rafael
5
2016
Connectedness of the space of smooth actions of \(\mathbb{Z}^{n}\) on the interval. Zbl 1375.37081
Bonatti, Christian; Eynard-Bontemps, Hélène
1
2016
A spectral-like decomposition for transitive Anosov flows in dimension three. Zbl 1384.37038
Beguin, F.; Bonatti, C.; Yu, B.
1
2016
Dominated chain recurrent class with singularities. Zbl 1371.37027
Bonatti, Christian; Gan, Shaobo; Yang, Dawei
5
2015
Centralizers of \(C^1\)-contractions of the half line. Zbl 1326.22019
Bonatti, Christian; Farinelli, Églantine
2
2015
Flexible periodic points. Zbl 1352.37076
Bonatti, Christian; Shinohara, Katsutoshi
2
2015
Robust vanishing of all Lyapunov exponents for iterated function systems. Zbl 1284.37044
Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J.
8
2014
Smooth conjugacy classes of circle diffeomorphisms with irrational rotation number. Zbl 1346.37045
Bonatti, Christian; Guelman, Nancy
2
2014
Tame dynamics and robust transitivity chain-recurrence classes versus homoclinic classes. Zbl 1309.37025
Bonatti, C.; Crovisier, S.; Gourmelon, N.; Potrie, R.
1
2014
The \(C^{1+\alpha}\) hypothesis in Pesin theory revisited. Zbl 1312.37018
Bonatti, Christian; Crovisier, Sylvain; Shinohara, Katsutoshi
10
2013
Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication. Zbl 1303.37008
Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Gourmelon, N.
9
2013
A robustly chain transitive attractor with singularities of different indices. Zbl 1304.37002
Bonatti, Christian; Li, Ming; Yang, Dawei
5
2013
On the existence of attractors. Zbl 1272.37019
Bonatti, Christian; Li, Ming; Yang, Dawei
5
2013
Abundance of \(C^{1}\)-robust homoclinic tangencies. Zbl 1300.37013
Bonatti, Christian; Díaz, Lorenzo J.
19
2012
Stabilization of heterodimensional cycles. Zbl 1284.37020
Bonatti, C.; Díaz, L. J.; Kiriki, S.
14
2012
Perturbation of the Lyapunov spectra of periodic orbits. Zbl 1268.37027
Bochi, J.; Bonatti, C.
12
2012
Fragile cycles. Zbl 1279.37022
Bonatti, Ch.; Díaz, L. J.
2
2012
Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms. Zbl 1246.37040
Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain
62
2011
Towards a global view of dynamical systems, for the \(C^{1}\)-topology. Zbl 1256.37006
Bonatti, C.
19
2011
Quasi-orbit spaces associated to \(T_0\)-spaces. Zbl 1218.54025
Bonatti, C.; Hattab, H.; Salhi, E.
4
2011
Hasse diagrams and orbit class spaces. Zbl 1213.54050
Bonatti, C.; Hattab, H.; Salhi, E.; Vago, G.
3
2011
Non-hyperbolic ergodic measures with large support. Zbl 1195.37013
Bonatti, Christian; Díaz, Lorenzo J.; Gorodetski, Anton
16
2010
Statistical behaviour of the leaves of Riccati foliations. Zbl 1209.37055
Bonatti, Ch.; Gómez-Mont, X.; Vila-Freyer, R.
9
2010
Axiom A diffeomorphisms derived from Anosov flows. Zbl 1201.37033
Bonatti, Christian; Guelman, Nancy
6
2010
The \(C^1\) generic diffeomorphism has trivial centralizer. Zbl 1177.37025
Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie
12
2009
On the hyperbolicity of homoclinic classes. Zbl 1200.37023
Bonatti, Christian; Gan, Shaobo; Yang, Dawei
9
2009
Roots in the mapping class groups. Zbl 1160.57014
Bonatti, Christian; Paris, Luis
5
2009
Transitive Anosov flows and Axiom-A diffeomorphisms. Zbl 1173.37028
Bonatti, Christian; Guelman, Nancy
3
2009
Robust heterodimensional cycles and \(C^1\)-generic dynamics. Zbl 1156.37004
Bonatti, Christian; Díaz, Lorenzo J.
33
2008
Local density of diffeomorphisms with large centralizers. Zbl 1163.58003
Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie
10
2008
\(C^1\)-generic conservative diffeomorphisms have trivial centralizer. Zbl 1149.37017
Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie
6
2008
3-manifolds which are orbit spaces of diffeomorphisms. Zbl 1165.37001
Bonatti, C.; Paoluzzi, L.
5
2008
Super exponential growth of the number of periodic orbits inside homoclinic classes. Zbl 1145.37015
Bonatti, Christian; Díaz, Lorenzo J.; Fisher, Todd
4
2008
The centralizer of a \(C^1\)-generic diffeomorphism is trivial. Zbl 1149.37012
Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie
2
2008
Periodic points and homoclinic classes. Zbl 1144.37007
Abdenur, F.; Bonatti, Ch.; Crovisier, S.; Díaz, L. J.; Wen, L.
31
2007
On the existence of non-trivial homoclinic classes. Zbl 1128.37021
Bonatti, Christian; Gan, Shaobo; Wen, Lan
11
2007
Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices. Zbl 1153.37340
Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pochinka, O. V.
6
2007
Perturbations of the derivative along periodic orbits. Zbl 1175.37027
Bonatti, Christian; Gourmelon, Nikolas; Vivier, Thérèse
36
2006
Classification of Morse-Smale diffeomorphisms with the chain of saddles on 3-manifolds. Zbl 1222.37021
Bonatti, Christian; Grines, Viacheslav; Pochinka, Olga
6
2006
Global dominated splittings and the \( C^1\) Newhouse phenomenon. Zbl 1088.37013
Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain
5
2006
Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective. Zbl 1060.37020
Bonatti, Christian; Díaz, Lorenzo J.; Viana, Marcelo
200
2005
Transitive partially hyperbolic diffeomorphisms on 3-manifolds. Zbl 1074.57015
Bonatti, Christian; Wilkinson, Amie
27
2005
Classification of Morse-Smale diffeomorphisms with a finite set of heteroclinic orbits on 3-manifolds. Zbl 1138.37307
Bonatti, C.; Grines, V. Z.; Pochinka, O. V.
17
2005
Generic symplectic dynamics. Zbl 1084.37017
Arnaud, Marie-Claude; Bonatti, Christian; Crovisier, Sylvain
14
2005
Generic diffeomorphisms on compact surfaces. Zbl 1089.37032
Abdenur, Flavio; Bonatti, Christian; Crovisier, Sylvain; Díaz, Lorenzo J.
11
2005
Recurrence and genericity. Zbl 1071.37015
Bonatti, Christian; Crovisier, Sylvain
105
2004
Lyapunov exponents with multiplicity 1 for deterministic products of matrices. Zbl 1087.37017
Bonatti, C.; Viana, M.
22
2004
Topological classification of gradient-like diffeomorphisms on 3-manifolds. Zbl 1056.37023
Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E.
20
2004
Non-wandering sets with non-empty interiors. Zbl 1083.37020
Abdenur, Flavio; Bonatti, Christian; Díaz, Lorenzo J.
14
2004
Abundance of stable ergodicity. Zbl 1052.37023
Bonatti, Christian; Matheus, Carlos; Viana, Marcelo; Wilkinson, Amie
6
2004
A Hölder continuous vector field tangent to many foliations. Zbl 1147.37313
Bonatti, Christian; Franks, John
3
2004
Classification of Morse-Smale diffeomorphisms with finite sets of heteroclinic orbits on 3-manifolds. Zbl 1282.37022
Bonatti, Ch.; Grines, V. Z.; Pochina, O. V.
1
2004
A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources. Zbl 1049.37011
Bonatti, C.; Díaz, L. J.; Pujals, E. R.
110
2003
Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices. (Genericity of non-zero Lyapunov exponents for deterministic products of matrices). Zbl 1025.37018
Bonatti, Christian; Gómez-Mont, Xavier; Viana, Marcelo
38
2003
Removing zero Lyapunov exponents. Zbl 1048.37026
Baraviera, Alexandre T.; Bonatti, Christian
29
2003
Robustly transitive sets and heterodimensional cycles. Zbl 1056.37024
Bonatti, Christian; Díaz, Lorenzo J.; Pujals, Enrique R.; Rocha, Jorge
16
2003
Topological equivalence of saddle connections in dimension 3. Zbl 1056.37030
Bonatti, Christian; Dufraine, Emmanuel
5
2003
Recurrence and genericity. Zbl 1027.37011
Bonatti, Christian; Crovisier, Sylvain
3
2003
On maximal transitive sets of generic diffeomorphisms. Zbl 1032.37011
Bonatti, Christian; Dıaz, Lorenzo J.
21
2002
Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves. Zbl 1157.37309
Bonatti, C.; Grines, V.; Medvedev, V.; Pécou, E.
20
2002
Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms. Zbl 1031.37030
Bonatti, Christian; Díaz, Lorenzo J.; Ures, Raúl
18
2002
Smale flows in dimension 3: finite presentations of invariant neighbourhoods of saddle sets. Zbl 1102.37307
Béguin, F.; Bonatti, C.
10
2002
On Morse-Smale diffeomorphisms without heteroclinic intersections on three-manifolds. Zbl 1011.37013
Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pécou, E.
6
2002
Two-dimensional links and diffeomorphisms on 3-manifolds. Zbl 1008.37013
Bonatti, Christian; Grines, Viatcheslav; Pécou, Elisabeth
6
2002
The index of stable critical points. Zbl 1013.37016
Bonatti, Christian; Villadelprat, Jordi
4
2002
\(C^1\)-generic dynamics: Tame and wild behaviour. Zbl 1136.37318
Bonatti, C.
1
2002
Statistical behaviour of the leaves of certain holomorphic foliations. Zbl 1010.37025
Bonatti, Christian; Gómez-Mont, Xavier
15
2001
On the topological classification of gradient-like diffeomorphisms without heteroclinic curves on three-dimensional manifolds. Zbl 1041.37007
Bonatti, C.; Grines, V. Z.; Medvedev, V. S.; Pecou, E.
6
2001
Dynamical systems in dimension 2 and 3: conjugacy invariants and classification. Zbl 1121.37306
Bonatti, C.; Grines, V.; Langevin, R.
4
2001
SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Zbl 0962.37012
Alves, José F.; Bonatti, Christian; Viana, Marcelo
129
2000
SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Zbl 0996.37033
Bonatti, Christian; Viana, Marcelo
104
2000
Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\). Zbl 0959.37017
Bonatti, C.; Grines, V.
41
2000
There is no “Shadowing lemma” for partially hyperbolic dynamics. Zbl 0973.37016
Bonatti, Christian; Díaz, Lorenzo J.; Turcat, Gaël
20
2000
Lorenz attractors with arbitrary expanding dimension. Zbl 0976.37014
Bonatti, Ch.; Pumariño, A.; Viana, M.
2
2000
Heteroclinic connections and genericity of infinitely many sinks and sources. Zbl 0944.37012
Bonatti, Christian; Díaz, Lorenzo
14
1999
Abnormal escape rates from nonuniformly hyperbolic sets. Zbl 0987.37018
Baladi, Viviane; Bonatti, Christian; Schmitt, Bernard
9
1999
Construction of 3-dimensional Smale flows. Zbl 0966.37003
Béguin, F.; Bonatti, C.; Vietez, J. L.
1
1999
Smale diffeomorphisms of surfaces. With the collab. of Emmanuelle Jeandenans. Zbl 0922.58058
Bonatti, C.; Langevin, R.
15
1998
Surface homeomorphisms with zero-dimensional singular set. Zbl 0929.37013
Bonatti, C.; Kolev, B.
3
1998
Cubic tangencies and hyperbolic diffeomorphisms. Zbl 0943.37012
Bonatti, Ch.; Díaz, L. J.; Vuillemin, F.
3
1998
...and 17 more Documents
all top 5

Cited by 647 Authors

46 Bonatti, Christian
37 Grines, Vyacheslav Zigmundovich
35 Pochinka, Olga Vital’evna
29 Lee, Manseob
23 Varandas, Paulo
22 Morales, Carlos Arnoldo
21 Bessa, Mário
21 Viana, Marcelo
19 Alves, José Ferreira
19 Medvedev, Vladislav Sergeevich
18 Araújo, Vítor
17 Crovisier, Sylvain
17 Díaz, Lorenzo Justiniano
17 Potrie, Rafael
17 Zhuzhoma, Evgeniĭ Viktorovich
16 Yang, Jiagang
15 Bochi, Jairo
14 Gan, Shaobo
14 Gelfert, Katrin Grit
14 Yang, Dawei
11 Tahzibi, Ali
10 Avila Cordeiro de Melo, Artur
10 Hammerlindl, Andy
10 Pacifico, Maria José
10 Pinheiro, Vilton
10 Tian, Xueting
9 Arbieto, Alexander
9 Barrientos, Pablo G.
9 Rocha, Jorge
9 Zhou, Yunhua
8 Alvarez, Sébastien
8 Gurevich, Elena Ya.
8 Luzzatto, Stefano
8 Sambarino, Martín
8 Sumi, Naoya
8 Sun, Wenxiang
7 Fakhari, Abbas
7 Hirsch, Morris W.
7 Liang, Chao
7 Pesin, Yakov Borisovich
7 Pujals, Enrique Ramiro
7 Rams, Michał
7 Wen, Xiao
7 Zhang, Jinhua
6 Bautista, Serafín
6 Climenhaga, Vaughn
6 Dolgopyat, Dmitry
6 Fisher, Todd L.
6 Gorodetski, Anton
6 Homburg, Ale Jan
6 Liao, Gang
6 Oliveira, Krerley
6 Rodriguez-Hertz, Federico
6 Rodriguez Hertz, Jana
6 Shi, Yi
6 Ures, Raúl
6 Wang, Xiaodong
6 Zhu, Yujun
5 Andersson, Martin
5 Backes, Lucas H.
5 Béguin, François
5 Blonigan, Patrick J.
5 Cao, Yongluo
5 Castro, Armando
5 Catalan, Thiago
5 Catsigeras, Eleonora
5 Gogolev, Andrey
5 Gómez-Mont, Xavier
5 Gourmelon, Nicolas
5 Kleptsyn, Victor A.
5 Krauskopf, Bernd
5 Laudenbach, François
5 Lee, Keonhee
5 Lopes Dias, João
5 Osinga, Hinke Maria
5 Rodrigues, Alexandre A. P.
5 Saghin, Radu
5 Salgado, Luciana
5 Santiago, Bruno
5 Shinohara, Katsutoshi
5 Sibony, Nessim
5 Turaev, Dmitry V.
5 Vásquez, Carlos H.
5 Wen, Lan
5 Yu, Bin
4 Abdenur, Flavio
4 Asaoka, Masayuki
4 Barbot, Thierry
4 Berger, Pierre
4 Da Luz, Adriana
4 Fenley, Sérgio R.
4 Firmo, Sebatião
4 Freitas, Jorge Milhazes
4 Hattab, Hawete
4 Hittmeyer, Stefanie
4 Horita, Vanderlei
4 Ilyashenko, Yulij Sergeevich
4 Kiriki, Shin
4 Kuznetsov, Sergey P.
4 Li, Ming
...and 547 more Authors
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Cited in 145 Serials

106 Ergodic Theory and Dynamical Systems
46 Discrete and Continuous Dynamical Systems
34 Proceedings of the American Mathematical Society
32 Journal of Differential Equations
31 Mathematische Zeitschrift
29 Dynamical Systems
27 Transactions of the American Mathematical Society
22 Communications in Mathematical Physics
20 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
19 Israel Journal of Mathematics
19 Proceedings of the Steklov Institute of Mathematics
17 Journal of Statistical Physics
16 Topology and its Applications
14 Advances in Mathematics
14 Acta Mathematica Sinica. English Series
14 Bulletin of the Brazilian Mathematical Society. New Series
12 Mathematical Notes
12 Nonlinearity
12 Annales de l’Institut Fourier
11 Inventiones Mathematicae
11 Journal of Dynamics and Differential Equations
11 Journal of Modern Dynamics
10 Qualitative Theory of Dynamical Systems
9 Stochastics and Dynamics
8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
8 Comptes Rendus. Mathématique. Académie des Sciences, Paris
7 Chaos, Solitons and Fractals
7 Journal of Mathematical Sciences (New York)
7 Geometry & Topology
7 Regular and Chaotic Dynamics
6 Functional Analysis and its Applications
6 Doklady Mathematics
6 Journal of the European Mathematical Society (JEMS)
5 Journal of Mathematical Analysis and Applications
5 Duke Mathematical Journal
5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
5 Journal of the Institute of Mathematics of Jussieu
4 Journal of Computational Physics
4 Commentarii Mathematici Helvetici
4 Publications Mathématiques
4 Monatshefte für Mathematik
4 Physica D
4 Geometric and Functional Analysis. GAFA
4 Nonlinear Dynamics
4 Journal of Dynamical and Control Systems
4 Advances in Difference Equations
4 Science China. Mathematics
3 Russian Mathematical Surveys
3 Acta Mathematica
3 Journal of the Mathematical Society of Japan
3 Mathematische Annalen
3 Michigan Mathematical Journal
3 Chinese Annals of Mathematics. Series B
3 The Journal of Geometric Analysis
3 Boletim da Sociedade Brasileira de Matemática. Nova Série
3 Journal of Inequalities and Applications
3 Chaos
3 Annals of Mathematics. Second Series
3 Portugaliae Mathematica. Nova Série
3 Axioms
3 Open Mathematics
3 Journal de l’École Polytechnique – Mathématiques
2 Communications on Pure and Applied Mathematics
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Fundamenta Mathematicae
2 Geometriae Dedicata
2 Journal für die Reine und Angewandte Mathematik
2 Proceedings of the London Mathematical Society. Third Series
2 Transactions of the Moscow Mathematical Society
2 Revista Matemática Iberoamericana
2 Journal of the American Mathematical Society
2 Bulletin of the American Mathematical Society. New Series
2 Topology Proceedings
2 Journal of Difference Equations and Applications
2 Annales Henri Poincaré
2 Differential Equations
2 Algebraic & Geometric Topology
2 SIAM Journal on Applied Dynamical Systems
1 Journal of Mathematical Physics
1 The Mathematical Intelligencer
1 Archiv der Mathematik
1 Bulletin de la Société Mathématique de France
1 Colloquium Mathematicum
1 Compositio Mathematica
1 Indiana University Mathematics Journal
1 Journal of Geometry
1 Journal of the Korean Mathematical Society
1 Journal of the London Mathematical Society. Second Series
1 Journal of Pure and Applied Algebra
1 Memoirs of the American Mathematical Society
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Osaka Journal of Mathematics
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Publications of the Research Institute for Mathematical Sciences, Kyoto University
1 Quaestiones Mathematicae
1 SIAM Journal on Numerical Analysis
1 Tokyo Journal of Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Probability Theory and Related Fields
...and 45 more Serials
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Cited in 42 Fields

771 Dynamical systems and ergodic theory (37-XX)
94 Manifolds and cell complexes (57-XX)
39 Ordinary differential equations (34-XX)
33 Differential geometry (53-XX)
29 Several complex variables and analytic spaces (32-XX)
28 General topology (54-XX)
25 Global analysis, analysis on manifolds (58-XX)
23 Measure and integration (28-XX)
18 Probability theory and stochastic processes (60-XX)
14 Group theory and generalizations (20-XX)
11 Mechanics of particles and systems (70-XX)
10 Functions of a complex variable (30-XX)
10 Statistical mechanics, structure of matter (82-XX)
9 Algebraic topology (55-XX)
6 Partial differential equations (35-XX)
5 Topological groups, Lie groups (22-XX)
5 Operator theory (47-XX)
4 Algebraic geometry (14-XX)
4 Linear and multilinear algebra; matrix theory (15-XX)
4 Difference and functional equations (39-XX)
3 Nonassociative rings and algebras (17-XX)
3 Real functions (26-XX)
3 Calculus of variations and optimal control; optimization (49-XX)
3 Numerical analysis (65-XX)
3 Fluid mechanics (76-XX)
3 Systems theory; control (93-XX)
2 Mathematical logic and foundations (03-XX)
2 Commutative algebra (13-XX)
2 Abstract harmonic analysis (43-XX)
2 Biology and other natural sciences (92-XX)
1 Combinatorics (05-XX)
1 General algebraic systems (08-XX)
1 Number theory (11-XX)
1 Associative rings and algebras (16-XX)
1 Category theory; homological algebra (18-XX)
1 \(K\)-theory (19-XX)
1 Potential theory (31-XX)
1 Statistics (62-XX)
1 Computer science (68-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Quantum theory (81-XX)
1 Geophysics (86-XX)

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