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摘要
In this paper we study a skew product map F preserving an ergodic measure mu of positive entropy. We show that if on the fibers the map are C1+alpha diffeomorphisms with nonzero Lyapunov exponents, then F has ergodic measures of arbitrary intermediate entropies. To construct these measures we find a set on which the return map is a skew product with horseshoes along fibers. We can control the average return time and show the maximal entropy of these measures can be arbitrarily close to h(mu)(F).
- 出版日期2010-7
