Smoothness of solenoidal attractors

Artur Avila, Sébastien Gouëzel, Masato Tsujii

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We consider dynamical systems generated by skew products of affine contractions on the real line over angle-multiplying maps on the circle S 1: T-.S1 X ℝ-.S1 × ℝ, T(x,y) = (ℓx, λy +f /(x)) where ≥ 2, 0 < λ < 1 and f is a Cr function on S1. We show that, if λ 1+2s > 1 for some 0 * s < r - 2, the density of the SBR measure for T is contained in the Sobolev space Ws(S1 ×ℝ) for almost all (Crgeneric, at least) f.

Original languageEnglish
Pages (from-to)21-35
Number of pages15
JournalDiscrete and Continuous Dynamical Systems
Volume15
Issue number1
DOIs
Publication statusPublished - May 2006
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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