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

DOI10.1007/BF02698771zbMath0542.58027MaRDI QIDQ795396

Charles C. Pugh

Publication date: 1984

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1984__59__143_0

zbMATH Keywords

diffeomorphismstable manifold

Mathematics Subject Classification ID

Differentiable maps on manifolds (58C25) Dynamical systems with hyperbolic behavior (37D99)

Related Items

Smoothness of invariant manifolds for nonautonomous equations ⋮ Notes on a study of vector bundle dynamical systems. II: 1 ⋮ Notes on a study of vector bundle dynamical systems II: 2 ⋮ Ergodic Attractors ⋮ Stable manifolds and nonuniform hyperbolicity: optimal estimates ⋮ The almost Borel structure of surface diffeomorphisms, Markov shifts and their factors ⋮ Dominated Pesin theory: convex sum of hyperbolic measures ⋮ Stable minimality of expanding foliations ⋮ Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov ⋮ The Weil-Petersson geodesic flow is ergodic ⋮ The Lyapunov exponents of \(C^{1}\) hyperbolic systems ⋮ Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms ⋮ Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems ⋮ Statistical properties of chaotic systems ⋮ Weak pseudo-physical measures and Pesin’s entropy formula for Anosov 𝐶¹-diffeomorphisms. ⋮ Approximation of Bernoulli measures for non-uniformly hyperbolic systems ⋮ Beyond topological hyperbolicity: the L-shadowing property ⋮ Statistical decomposition of chaotic attractors by the eigenvectors of Oseledec matrix -- Active and passive information dynamics ⋮ A Franks’ lemma that preserves invariant manifolds ⋮ Minimality and stable bernoulliness in dimension 3 ⋮ 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 ⋮ The Pesin entropy formula for diffeomorphisms with dominated splitting ⋮ Lower bound in Pesin formula of C ¹ interval maps*

Cites Work

• Local \(C^n\) transformations of the real line
• Ergodic theory of differentiable dynamical systems
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• Generic Properties of Polynomial Vector Fields at Infinity
• Unnamed Item
• Unnamed Item