Lyapunov exponents of hyperbolic attractors

作者：Jiang DQ^*; Liu PD; Qian M

来源：Manuscripta Mathematica, 2002, 108(1): 43-67.

DOI：10.1007/s002290200254

Let mu(+) be the SBR measure on a hyperbolic attractor Omega of a C-2 Axiom A diffeomorphism (M, f) and v the volume measure on M. As is known, mu(+)-almost every x is an element of Omega is Lyapunov regular and the Lyapunov characteristic exponents of (f, Df) at x are constants lambda((i)) (mu(+), f), 1 less than or equal to i less than or equal to s. In this paper we prove that v-almost every x in the basin of attraction W-s(Q) is positively regular and the Lyapunov characteristic exponents of (f, Df) at x are the constants lambda(1) (mu(+), f), (. . .), lambda((s)) (mu(+), f). Similar results are also obtained for nonuniformly completely hyperbolic attractors.

• 出版日期2002-5
• 单位北京大学