Stochastic perturbations of fat solenoidal attractors
Consider a skew product transformation, consisting of an angle multiplication by an integer \(l\geq2\) on the unit circle as the base system, and an affine contraction with coefficient \(0<\lambda<1\) of the real line as the fibre system. The base dynamics is assumed to enter the fibre dynamics additively as a \(C^r\), \(r\geq3\), function of the base state. In case that \(\lambda l>1\), i.e.\ if the system is locally area expanding, it is known that there exists an SRB measure which is absolutely continuous with respect to the Lebesgue measure. The present paper gives conditions for the stability of the SRB measure and of its ergodic properties with respect to small stochastic perturbations.
scientific article; zbMATH DE number 5795522
scientific article