Random perturbations of Axiom A basic sets (Q1284780)

This paper concerns random dynamical systems (RDS) generated by small random, diffeomorphism-type perturbations of an Axiom A basic set of a deterministic diffeomorphism. The author is mainly interested in the dynamical properties of such an RDS near the basic set. First of all, the author discusses the structural stability of a hyperbolic set with respect to such time-dependent perturbations. Using the structural stability results and the Markov partition method, the author gives a symbolic representation of the RDS described above when the hyperbolic set is an Axiom A basic set. This enables to apply the thermodynamic formalism of random subshifts of finite type.