The entropy of 𝐶¹-diffeomorphisms without a dominated splitting

DOI10.1090/tran/7380zbMath1402.37026arXiv1606.01765OpenAlexW2963028229MaRDI QIDQ4567902

Todd Fisher, Sylvain Crovisier, Jérôme Buzzi

Publication date: 20 June 2018

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

Full work available at URL: https://arxiv.org/abs/1606.01765

zbMATH Keywords

topological entropyLyapunov exponentdominated splittinghomoclinic classhomoclinic tangencymeasure-theoretic entropy

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Topological entropy (37B40) Dynamical systems with hyperbolic orbits and sets (37D05) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (14)

Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov ⋮ Topological pressure for conservative C ¹ -diffeomorphisms with no dominated splitting ⋮ Upper bounds on measure-theoretic tail entropy for dominated splittings ⋮ Approximation property on entropies for surface diffeomorphisms ⋮ Entropy of partially hyperbolic flows with center dimension two ⋮ Homoclinic tangency and variation of entropy ⋮ Periodic points and measures for a class of skew-products ⋮ Symbolic extensions for 3-dimensional diffeomorphisms ⋮ Topological entropy on points without physical-like behaviour ⋮ Statistical properties of physical-like measures* ⋮ Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems ⋮ On the continuity of topological entropy of certain partially hyperbolic diffeomorphisms ⋮ Historic wandering domains near cycles ⋮ Stable intersection of Cantor sets in higher dimension and robust homoclinic tangency of the largest codimension

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