On the stable ergodicity of diffeomorphisms with dominated splitting

DOI10.1088/1361-6544/aaea93zbMath1410.37030arXiv1806.03089OpenAlexW3105032500WikidataQ128686458 ScholiaQ128686458MaRDI QIDQ4614992

D. J. Obata

Publication date: 1 February 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.03089

zbMATH Keywords

dominated splittingstable ergodicityweak partial hyperbolicity

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (2)

Minimality and stable bernoulliness in dimension 3 ⋮ New examples of stably ergodic diffeomorphisms in dimension 3

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Partially hyperbolic diffeomorphisms with a trapping property
• Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms
• Diffeomorphisms with positive metric entropy
• Partial hyperbolicity far from homoclinic bifurcations
• On the regularization of conservative maps
• Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms
• New criteria for ergodicity and nonuniform hyperbolicity
• On the ergodicity of partially hyperbolic systems
• Topological transitivity of one class of dynamical systems and flows of frames on manifolds of negative curvature
• Partial hyperbolicity, Lyapunov exponents and stable ergodicity
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Stable ergodicity and julienne quasi-conformality
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• Stably ergodic diffeomorphisms
• Stably ergodic diffeomorphisms which are not partially hyperbolic
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• Entropic stability beyond partial hyperbolicity
• The Bernoulli property for weakly hyperbolic systems
• A pasting lemma and some applications for conservative systems
• SOME SMOOTH ERGODIC SYSTEMS
• Invariant manifolds
• Recurrence and genericity

This page was built for publication: On the stable ergodicity of diffeomorphisms with dominated splitting