Ergodic Hyperbolic Attractors of Endomorphisms

Author： Jiang Da-Quan   Qian Min  

Publisher： Springer Publishing Company

ISSN： 1079-2724

Source： Journal of Dynamical and Control Systems, Vol.12, Iss.4, 2006-10, pp. : 465-488

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Abstract

Let  be an SRB-measure on an Axiom A attractor Δ of a C 2-endomorphism (M, f). As is known, -almost every x Δ is positively regular and the Lyapunov exponents of (f, T f) at x are constants (i)(f, ), 1 ≤ i ≤ s. In this paper, we prove that Lebesgue-almost every x in a small neighborhood of Δ is positively regular and the Lyapunov exponents of (f, T f) at x are the constants (i)(f, ), 1 ≤ i ≤ s. This result is then generalized to nonuniformly completely hyperbolic attractors of endomorphisms. The generic property of SRB-measures is also proved.

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