The \(C^{1+\alpha}\) hypothesis in Pesin theory revisited

DOI10.3934/jmd.2013.7.605zbMath1312.37018arXiv1306.6391OpenAlexW3099090350MaRDI QIDQ2437969

Katsutoshi Shinohara, Sylvain Crovisier, Christian Bonatti

Publication date: 10 March 2014

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.6391

zbMATH Keywords

Lyapunov exponentsdominated splittingPesin theorywild diffeomorphism

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Generic properties, structural stability of dynamical systems (37C20) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Infinite nonwandering sets arising in bifurcations of dynamical systems (37G30) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

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Livšic theorem for low-dimensional diffeomorphism cocycles ⋮ Horseshoes for diffeomorphisms preserving hyperbolic measures ⋮ The almost Borel structure of surface diffeomorphisms, Markov shifts and their factors ⋮ Dominated Pesin theory: convex sum of hyperbolic measures ⋮ Local perturbations of conservativeC¹diffeomorphisms ⋮ Chaotic dynamics of spatially homogeneous spacetimes ⋮ Sinks and sources for \(C^1\) dynamics whose Lyapunov exponents have constant sign ⋮ Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases ⋮ Approximation of Bernoulli measures for non-uniformly hyperbolic systems ⋮ Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes ⋮ Periodic measures and partially hyperbolic homoclinic classes ⋮ Local stable and unstable sets for positive entropy \(C^1\) dynamical systems ⋮ The existence of semi-horseshoes for \(C^1\) partially hyperbolic attractors in a Banach space ⋮ Hyperbolic sets and entropy at the homological level ⋮ Lower bound in Pesin formula of C ¹ interval maps*

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