Generic diffeomorphisms on compact surfaces

DOI10.4064/fm187-2-3zbMath1089.37032OpenAlexW2090081609MaRDI QIDQ5469388

Flavio Abdenur, Sylvain Crovisier, Christian Bonatti, Lorenzo J. Dıaz

Publication date: 18 May 2006

Published in: Fundamenta Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/fm187-2-3

zbMATH Keywords

filtrationAnosov diffeomorphismshyperbolicitySmale's conjecturedominated splittinghomoclinic classsurface diffeomorphismhomoclinic tangencies\(C^1\)-generic approachchain-recurrence class

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Generic properties, structural stability of dynamical systems (37C20) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (13)

Ergodic optimization for some dynamical systems beyond uniform hyperbolicity ⋮ Periodic orbits and chain-transitive sets of \(C^1\)-diffeomorphisms ⋮ Another dichotomy for surface diffeomorphisms ⋮ Dominated splitting of differentiable dynamics with \(\mathrm{C}^1\)-topological weak-star property ⋮ SURVEY Towards a global view of dynamical systems, for the C¹-topology ⋮ Codimension one generic homoclinic classes with interior ⋮ Purely imaginary eigenvalues from homoclinic tangencies ⋮ On Araujo's theorem for flows ⋮ Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes ⋮ Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes ⋮ Robustly non-hyperbolic transitive endomorphisms on 𝕋² ⋮ Abundance of $C^{1}$-robust homoclinic tangencies ⋮ Measures of maximal entropy for surface diffeomorphisms

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