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.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics