A genericC1map has no absolutely continuous invariant probability measure

DOI10.1088/0951-7715/19/11/011zbMath1190.37018OpenAlexW2597963304MaRDI QIDQ3417593

Jairo Bochi, Artur Avila

Publication date: 29 January 2007

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/19/11/011

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40)

Related Items (12)

Degree of recurrence of generic diffeomorphisms ⋮ Pesin's entropy formula for \(C^1\) non-uniformly expanding maps ⋮ Higher-dimensional attractors with absolutely continuous invariant probability ⋮ (Semi)continuity of the entropy of Sinai probability measures for partially hyperbolic diffeomorphisms ⋮ Existence of SRB measures for hyperbolic maps with weak regularity ⋮ A Rokhlin lemma for noninvertible totally-ordered measure-preserving dynamical systems ⋮ Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms ⋮ Empiric Stochastic Stability of Physical and Pseudo-physical Measures ⋮ STABLE SETS OF CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE THE EXPECTED DIMENSION ⋮ Local entropy via preimage structure ⋮ On Li-Yorke measurable sensitivity ⋮ The Pesin entropy formula for diffeomorphisms with dominated splitting

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