Lyapunov exponents of hyperbolic attractors

Abstract

 Let μ ₊ be the SBR measure on a hyperbolic attractor Ω of a C ² Axiom A diffeomorphism (M,f) and v the volume measure on M. As is known, μ ₊ -almost every is Lyapunov regular and the Lyapunov characteristic exponents of (f,Df) at x are constants $\lambda^{(i)}(\mu_+,f),1\leq i\leq s$. In this paper we prove that $v$-almost every $x$ in the basin of attraction $W^s(\Omega)$ is positively regular and the Lyapunov characteristic exponents of $(f,Df)$ at $x$ are the constants . Similar results are also obtained for nonuniformly completely hyperbolic attractors.