Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato Smoothness of solenoidal attractors. (English) Zbl 1106.37015 Discrete Contin. Dyn. Syst. 15, No. 1, 21-35 (2006). The authors deal with dynamical systems generated by skew products of affine contractions on the real line over angle-multiplying maps on the circle \(S^1= \mathbb{R}/\mathbb{Z}\): \[ T: S^1\times\mathbb{R}\to S^1\times\mathbb{R},\quad T(x,y)= (\ell x,\lambda y+ f(x)), \] where \(\ell\geq 2\) is an integer, \(\lambda\in (0,1)\) and \(f\in C^r(S^1)\), \(r> 3\). The authors study the smoothness of the density of the SBR measure in more detail, and the mixing properties of \(T\). Reviewer: Messoud A. Efendiev (Berlin) Cited in 10 Documents MSC: 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems 37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. 37A25 Ergodicity, mixing, rates of mixing 37E10 Dynamical systems involving maps of the circle Keywords:skew-product; mixing property; SBR measure; maps on the circle PDF BibTeX XML Cite \textit{A. Avila} et al., Discrete Contin. Dyn. Syst. 15, No. 1, 21--35 (2006; Zbl 1106.37015) Full Text: DOI