On the hyperbolicity of \(\operatorname{C}^1\)-generic homoclinic classes

DOI10.1016/j.crma.2015.07.017zbMath1332.37020arXiv1412.4656OpenAlexW2635034612MaRDI QIDQ5965061

Xiaodong Wang

Publication date: 2 March 2016

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.4656

Mathematics Subject Classification ID

Dynamical systems with hyperbolic orbits and sets (37D05) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Cites Work

• Unnamed Item
• Periodic orbits and chain-transitive sets of \(C^1\)-diffeomorphisms
• The selecting lemma of Liao
• On the hyperbolicity of homoclinic classes
• A proof of the \(C^ 1\) stability conjecture
• A uniform \(C^1\) connecting lemma.
• Heteroclinic cycles and homoclinic closures for generic diffeomorphisms
• An ergodic closing lemma
• Partial hyperbolicity and homoclinic tangencies
• Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies
• Unfolding homoclinic tangencies inside horseshoes: hyperbolicity, fractal dimensions and persistent tangencies
• Expansive homoclinic classes
• Diffeomorphisms in ℱ¹(M) satisfy Axiom A
• 𝐶¹ Connecting Lemmas
• The set of axiom A diffeomorphisms with no cycles
• Necessary Conditions for Stability of Diffeomorphisms
• Recurrence and genericity
• Invariant manifolds

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