Diffeomorphisms with global dominated splittings cannot be minimal

DOI10.1090/S0002-9939-2011-10956-0zbMath1257.37025arXiv1011.2844MaRDI QIDQ3116548

Peng Fei Zhang

Publication date: 24 February 2012

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

Full work available at URL: https://arxiv.org/abs/1011.2844

zbMATH Keywords

minimaldominated splittingperiodic shadowingLiao's selecting lemmaLiao's sifting lemma

Mathematics Subject Classification ID

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (3)

On the dominated splitting of Lyapunov stable aperiodic classes ⋮ A shadowing lemma for quasi-hyperbolic strings of flows ⋮ Hyperbolicity for conservative diffeomorphisms

Cites Work

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• Area-preserving surface diffeomorphisms
• The selecting lemma of Liao
• Density of accessibility for partially hyperbolic diffeomorphisms with one-dimensional center
• Contributions to the stability conjecture
• Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
• A generalized shadowing lemma
• On the dynamics of dominated splitting
• Construction d'un difféomorphisme minimal d'entropie topologique non nulle
• Adapted metrics for dominated splittings

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