Non Uniform Hyperbolicity in Global Dynamics

Mildly dissipative diffeomorphisms of the disk with zero entropy

Author(s): Crovisier, Sylvain; Pujals, Enrique; Tresser, Charles
Published in: Acta Mathematica (to appear), 2020
Publisher: P

Symbolic dynamics for large non-uniformly hyperbolic sets of three dimensional flows

Author(s): Jerome Buzzi, Sylvain Crovisier, Yuri Lima
Published in: 2023
Publisher: ArXiv

Ergodic properties of multi-singular hyperbolic vector fields

Author(s): Sylvain Crovisier, Xiaodong Wang, Dawei Yang, Jinhua Zhang
Published in: 2023
Publisher: ArXiv

Doubly Intermittent Full Branch Maps with Critical Points and Singularities

Author(s): Douglas Coates, Stefano Luzzatto, Muhammad Mubarak
Published in: 2022
Publisher: ArXiv

Diffusion rate in non-generic directions in the wind-tree model

Author(s): Sylvain Crovisier, Pascal Hubert, Erwan Lanneau, Angel Pardo
Published in: 2023
Publisher: ArXiv

Random product of quasi-periodic cocycles

Author(s): Bezerra, Jamerson; Poletti, Mauricio
Published in: Proc. Amer. Math. Soc., 2021, Page(s) 2927--2942
Publisher: P
DOI: 10.1090/proc/15428

Accessibility for dynamically coherent partially hyperbolic diffeomorphisms with 2D center

Author(s): Martin Leguil, Luis Pedro Pineyrua
Published in: 2022
Publisher: ArXiv

Homoclinic tangencies and singular hyperbolicity for three-dimensional vector fields

Author(s): Crovisier, Sylvain; Yang, Dawei
Published in: Arxiv, 2021
Publisher: ArXiv
DOI: 10.48550/arXiv.1702.05994

Regularity of conjugacies of linearizable generalized interval exchange transformations

Author(s): Selim Ghazouani, Corinna Ulcigrai
Published in: 2023
Publisher: ArXiv

Persistent Non-Statistical Dynamics in One-Dimensional Maps

Author(s): Douglas Coates, Stefano Luzzatto
Published in: 2023
Publisher: ArXiv

Symbolic dynamics for nonuniformly hyperbolic maps with singularities in high dimension

Author(s): Araujo, Ermerson; Lima, Yuri; Poletti, Mauricio
Published in: Memoirs of the American Mathematical Society (to appear), 2020
Publisher: P

Nonlinear thermodynamicalformalism

Author(s): Buzzi, Jérôme; Leplaideur, Renaud
Published in: Annales Henri Lebesgue (to appear), 2020
Publisher: P

Rigidity of u-gibbs measures near conservative Anosov diffeomorphisms on T3

Author(s): Sebastien Alvarez ; Martin Leguil ; Davi Obata ; Bruno Santiago
Published in: 2022
Publisher: ArXiv

Closed geodesics in dilation surfaces

Author(s): Adrien Boulanger, Selim Ghazouani, Guillaume Tahar
Published in: 2021
Publisher: ArXiv

Uniqueness of u-Gibbs measures for hyperbolic skew products on T4

Author(s): Sylvain Crovisier, Davi Obata, Mauricio Poletti
Published in: 2022
Publisher: ArXiv

Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes

Author(s): Xiaodong Wang, Jinhua Zhang
Published in: Journal of Dynamics and Differential Equations, Issue 32/2, 2020, Page(s) 631-664, ISSN 1040-7294
Publisher: Plenum Publishers
DOI: 10.1007/s10884-019-09752-3

A new example of robustly transitive diffeomorphism

Author(s): Carrasco, Pablo D.; Obata, Davi
Published in: Math. Res. Lett., Issue 28, 2019, ISSN 1073-2780
Publisher: Mathematical Publishing
DOI: 10.4310/mrl.2021.v28.n3.a2

Uniqueness of the measure of maximal entropy for the standard map

Author(s): Obata, Davi
Published in: Comment. Math. Helv., Issue 96, 2020, ISSN 0010-2571
Publisher: Birkhauser Verlag
DOI: 10.4171/cmh/508

Symplectomorphisms with positive metric entropy

Author(s): Avila, Artur; Crovisier, Sylvain; Wilkinson, Amie
Published in: Proc. Lond. Math. Soc., Issue 124, 2019, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.12437

"Invariant graphs and spectral type of Schr\""odinger operators"

Author(s): Avila, Artur; Khanin, Konstantin; Leguil, Martin
Published in: Pure and Applied Functional Analysis, Issue 5, 2021, ISSN 2189-3756
Publisher: Yokohama Publishers

Open sets of partially hyperbolic skew products having a unique SRB measure

Author(s): Davi Obata
Published in: Advances in Mathematics, Issue 427, 2021, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2023.109136

Finiteness of partially hyperbolic attractors with one-dimensional center

Author(s): Sylvain CROVISIER, Rafael POTRIE, Martín SAMBARINO
Published in: Annales scientifiques de l'École normale supérieure, Issue 53/3, 2020, Page(s) 559-588, ISSN 0012-9593
Publisher: Elsevier BV
DOI: 10.24033/asens.2428

On the notions of singular domination and (multi-)singular hyperbolicity

Author(s): Sylvain Crovisier, Adriana da Luz, Dawei Yang, Jinhua Zhang
Published in: Science China Mathematics, Issue 63/9, 2020, Page(s) 1721-1744, ISSN 1674-7283
Publisher: Zhongguo Kexue Zazhishe/Science in China Press
DOI: 10.1007/s11425-019-1764-x

Empirical Measures of Partially Hyperbolic Attractors

Author(s): Sylvain Crovisier, Dawei Yang, Jinhua Zhang
Published in: Communications in Mathematical Physics, Issue 375/1, 2020, Page(s) 725-764, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-019-03668-1

Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center

Author(s): Christian Bonatti, Jinhua Zhang
Published in: Science China Mathematics, Issue 63/9, 2020, Page(s) 1647-1670, ISSN 1674-7283
Publisher: Zhongguo Kexue Zazhishe/Science in China Press
DOI: 10.1007/s11425-019-1751-2

Germ-typicality of the coexistence of infinitely many sinks

Author(s): Pierre Berger, Sylvain Crovisier, Enrique Pujals
Published in: Advances in Mathematics, Issue 407, 2022, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108528

Positive exponents for random products of conservative surface diffeomorphisms and some skew products

Author(s): Davi Obata, Mauricio Poletti
Published in: J. Dynam. Differential Equations, Issue 34, 2022, ISSN 1040-7294
Publisher: Plenum Publishers
DOI: 10.1007/s10884-021-10052-y

On the existence of SRB measures for C∞ surface diffeomorphisms

Author(s): Jérôme Buzzi, Sylvain Crovisier, Omri Sarig
Published in: International Mathematics Research Notices, Issue 2023/24, 2022, Page(s) 20812–20826, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnac275

Measures of maximal entropy for surface diffeomorphisms

Author(s): Buzzi, Jerome; Crovisier, Sylvain; Sarig, Omri
Published in: Annals of Mathematics, Issue 195, 2019, ISSN 0003-486X
Publisher: Princeton University Press
DOI: 10.4007/annals.2022.195.2.2

Cr-prevalence of stable ergodicity for a class of partially hyperbolic systems

Author(s): Martin Leguil ; Zhiyuan Zhang
Published in: J. Eur. Math. Soc., Issue 24, 2022, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1163

Uniqueness of minimal unstable lamination for discretized Anosov flows

Author(s): Nancy Guelman, Santiago Martinchich
Published in: Mathematische Zeitschrift, Issue 300, 2022, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-021-02827-2

Robust transitivity of singular hyperbolic attractors

Author(s): Sylvain Crovisier, Dawei Yang
Published in: Mathematische Zeitschrift, 2021, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-020-02618-1

Local perturbations of conservative C1 diffeomorphisms

Author(s): Jérôme Buzzi, Sylvain Crovisier, Todd Fisher
Published in: Nonlinearity, Issue 30/9, 2017, Page(s) 3613-3636, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/aa803f

Global stability of discretized Anosov flows

Author(s): Santiago Martinchich
Published in: Journal of Modern Dynamics, Issue 19, 2023, ISSN 1930-5311
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/jmd.2023016

On the centralizer of vector fields: criteria of triviality and genericity results

Author(s): Martin Leguil, Davi Obata, Bruno Santiago
Published in: Mathematische Zeitschrift, Issue 297/1-2, 2021, Page(s) 283-337, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-020-02511-x

Symmetries of vector fields: the diffeomorphism centralizer

Author(s): Obata, Davi
Published in: Discrete Contin. Dyn. Syst., Issue 41, 2019, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2021063

C1 density of stable ergodicity

Author(s): Artur Avila ; Sylvain Crovisier ; Amie Wilkinson
Published in: Advances in Math., Issue 379, 2021, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2020.107496

New examples of stably ergodic diffeomorphisms in dimension 3

Author(s): Gabriel Nuñez, Davi Obata, Jana Rodriguez-Hertz
Published in: Nonlinearity, Issue 34, 2020, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/abbab3

The entropy of $C^1$-diffeomorphisms without a dominated splitting

Author(s): Jérôme Buzzi, Sylvain Crovisier, Todd Fisher
Published in: Transactions of the American Mathematical Society, Issue 370/9, 2018, Page(s) 6685-6734, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7380

NON-HYPERBOLIC ERGODIC MEASURES AND HORSESHOES IN PARTIALLY HYPERBOLIC HOMOCLINIC CLASSES

Author(s): Dawei Yang, Jinhua Zhang
Published in: Journal of the Institute of Mathematics of Jussieu, 2019, Page(s) 1-28, ISSN 1474-7480
Publisher: Cambridge University Press
DOI: 10.1017/s1474748018000579

On the stable ergodicity of diffeomorphisms with dominated splitting

Author(s): Davi Obata
Published in: Nonlinearity, Issue 32/2, 2019, Page(s) 445-463, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/aaea93

Projective transformations of rotation sets

Author(s): François Béguin, Sylvain Crovisier, Frédéric Le Roux
Published in: Nonlinearity, Issue 32/4, 2019, Page(s) 1237-1241, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/aafcde

Strongly dissipative surface diffeomorphisms

Author(s): Sylvain Crovisier, Enrique Pujals
Published in: Commentarii Mathematici Helvetici, Issue 93/2, 2018, Page(s) 377-400, ISSN 0010-2571
Publisher: Birkhauser Verlag
DOI: 10.4171/cmh/438

Entropy rigidity for 3D conservative Anosov flows and dispersing billiards

Author(s): Jacopo De Simoi, Martin Leguil, Kurt Vinhage, Yun Yang
Published in: Geometric and Functional Analysis, Issue 30/5, 2020, Page(s) 1337-1369, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-020-00547-z

A priori bounds for GIETs, affine shadows and rigidity of foliations in genus 2

Author(s): Selim Ghazouani, Corinna Ulcigrai
Published in: Publ. Math. Inst. Hautes Études Sci., Issue 138, 2023, Page(s) 229–366, ISSN 0073-8301
Publisher: Springer Verlag
DOI: 10.1007/s10240-023-00142-6

Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds

Author(s): Jinhua Zhang
Published in: Journal of Modern Dynamics, Issue 17, 2021, ISSN 1930-5311
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/jmd.2021019

Continuity properties of Lyapunov exponents for surface diffeomorphisms

Author(s): Jerome Buzzi ; Sylvain Crovisier ; Omri Sarig
Published in: Inventiones Mathematicae, Issue 230, 2022, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-022-01132-x

On the Stable Ergodicity of Berger-Carrasco's example

Author(s): Obata, Davi
Published in: Ergodic Theory and Dynamical Systems, Issue 1, 2020, ISSN 0143-3857
Publisher: Cambridge University Press

Stable ergodicity and physical measures for weakly hyperbolic dynamical systems

Author(s): Obata, Davi dos Anjos
Published in: https://tel.archives-ouvertes.fr/tel-02457102, Issue 1, 2019
Publisher: Univ. Paris-Sud

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