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Smoothness of solenoidal attractors Artur Avila
 

Summary: Smoothness of solenoidal attractors
Artur Avila
, S´ebastien Gou¨ezel
and Masato Tsujii
February 24, 2005
Abstract
We consider dynamical systems generated by skew products of affine
contractions on the real line over angle-multiplying maps on the circle S1
:
T : S1
× R S1
× R, T(x, y) = ( x, y + f(x))
where 2, 0 < < 1 and f is a Cr
function on S1
. We show that, if
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 (Cr

  

Source: Avila, Artur - Instituto Nacional de Matemática Pura e Aplicada (IMPA)

 

Collections: Mathematics