Ergodic properties of smooth dynamical systems are considered. A point is called regular for an ergodic measure μ if it is generic for μ and the Lyapunov exponents at it coincide with those of μ. We show that an ergodic measure with no zero Lyapunov exponent is absolutely continuous with respect to unstable foliation [L] if and only if the set of all points which are regular for it has positive Lebesgue measure.
All Science Journal Classification (ASJC) codes
- 数学 (全般)