Lyapunov exponents of hyperbolic attractors

 Let μ+ be the SBR measure on a hyperbolic attractor Ω of a C2 Axiom A diffeomorphism (M,f) and v the volume measure on M. As is known, μ+-almost every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. Similar results are also obtained for nonuniformly completely hyperbolic attractors.