Another dichotomy for surface diffeomorphisms

DOI10.1090/S0002-9939-09-09879-7zbMath1173.37030OpenAlexW2012654725MaRDI QIDQ5322858

Carlos A. Morales

Publication date: 23 July 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-09-09879-7

zbMATH Keywords

Axiom A diffeomorphismcomplex eigenvalueshomoclinic tangency

Mathematics Subject Classification ID

Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Partially hyperbolic systems and dominated splittings (37D30)

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Purely imaginary eigenvalues from homoclinic tangencies ⋮ On Araujo's theorem for flows

Cites Work

• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
• An ergodic closing lemma
• Markov covers and finiteness of periodic attractors for diffeomorphisms with a dominated splitting
• Generic diffeomorphisms on compact surfaces
• Necessary Conditions for Stability of Diffeomorphisms