Non Uniform Hyperbolicity in Global Dynamics

Project Information

NUHGD

Grant agreement ID: 692925

DOI

10.3030/692925

Project closed

EC signature date 11 May 2016

Start date 1 September 2016

End date 31 August 2023

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 229 255,00

EU contribution

€ 1 229 255,00

Coordinated by

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Other (15)

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

Peer reviewed articles (33)

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

Thesis and dissertations (1)

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