Statistical stability of mostly expanding diffeomorphisms

Martin Andersson, CARLOS VASQUEZ EHRENFELD

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study how physical measures vary with the underlying dynamics in the open class of Cr, r>1, strong partially hyperbolic diffeomorphisms for which the central Lyapunov exponents of every Gibbs u-state is positive. If transitive, such a diffeomorphism has a unique physical measure that persists and varies continuously with the dynamics. A main ingredient in the proof is a new Pliss-like Lemma which, under the right circumstances, yields frequency of hyperbolic times close to one. Another novelty is the introduction of a new characterization of Gibbs cu-states. Both of these may be of independent interest. The non-transitive case is also treated: here the number of physical measures varies upper semi-continuously with the diffeomorphism, and physical measures vary continuously whenever possible.

Original languageEnglish
Pages (from-to)1245-1270
Number of pages26
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume37
Issue number6
DOIs
StatePublished - 1 Nov 2020
Externally publishedYes

Keywords

  • Lyapunov exponents
  • Partial hyperbolicity
  • SRB measures
  • Stable ergodicity
  • Statistical stability

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