Stably ergodic diffeomorphisms which are not partially hyperbolic

By A. Tahzibi. 2002

64 citations recorded by the source corpus.

We show stable ergodicity of a class of conservative diffeomorphisms ofTn which do not have any hyperbolic invariant subbundle. Moreover, the uniqueness of SRB (Sinai-Ruelle-Bowen) measure for non-conservativeC1 perturbations of such diffeomorphisms is verified. This class strictly contains non-partially hyperbolic robustly transitive diffeomorphisms constructed by Bonatti-Viana [4] and so we answer the question posed there on the stable ergodicity of such systems.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ba768026ac7955daf698d1d7339c4179ac3ecf04

Citations in the corpus

• New criteria for ergodicity and nonuniform hyperbolicity (2009, unknown): “Let us note that Tahzibi has already used hyperbolic periodic points to prove ergodicity in [36].”
• Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle (2006, unknown): “Let us also mention that there are already examples of conservative stably ergodic systems that are not partially hyperbolic [ 35 ].”
• On the regularization of conservative maps (2008, unknown): “But ∑ p∈P volF (s(W )) ∩ B(p, 1) = volF (s(W ))∩B = volW ∩B = ∑ p∈P volW∩B(p, 1), so we must have volF (s(W ))∩ B(p, 1) = volW ∩B(p, 1) also for p = p2n−k , and property (2) follows.”