Smoothness of solenoidal attractors (Q2503184)

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 \(T\).