Ergodic hyperbolic attractors of endomorphisms

Let mu be an SRB-measure on an Axiom A attractor Delta of a C(2)-endomorphism (M, f). As is known, p-almost every x is an element of Delta is positively regular and the Lyapunov exponents of (f, Tf) at x are constants lambda((i)) (f, mu), 1 <= i <= s. In this paper, we prove that Lebesgue-almost every x in a small neighborhood of Delta is positively regular and the Lyapunov exponents of (f, Tf) at x are the constants lambda((i)) (f, mu), 1 <= i <= s. This result is then generalized to nonuniformly completely hyperbolic attractors of endomorphisms. The generic property of SRB-measures is also proved.Automation & Control SystemsMathematics, AppliedSCI(E)EI0ARTICLE4465-4881