Smoothness of solenoidal attractors - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2006

Smoothness of solenoidal attractors

Résumé

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:S^{1}\times \R\to S^1\times \R, T(x,y)=(\ell x, \lambda y+f(x)) $ where $\ell\geq 2$, $0<\lambda<1$ and $f$ is a $C^r$ function on $S^1$. We show that, if $\lambda^{1+2s}\ell>1$ for some $0\leq s< r-2$, the density of the SBR measure for $T$ is contained in the Sobolev space $W^s(S^1\times \R)$ for almost all ($C^r$ generic, at least) $f$.

Dates et versions

hal-00012233 , version 1 (18-10-2005)

Identifiants

Citer

Artur Avila, Sebastien Gouezel, Masato Tsujii. Smoothness of solenoidal attractors. Discrete and Continuous Dynamical Systems - Series A, 2006, 15, pp.21-35. ⟨hal-00012233⟩
1981 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More