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Smoothness of solenoidal attractors. (English) Zbl 1106.37015
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 \(T\).

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
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