标题： 部分双曲微分同胚的简单李雅普诺夫谱 显示英文标题

标题： Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms

摘要： 我们研究部分双曲微分同胚的Lyapunov谱的简单性。 我们证明了一类保持体积的部分双曲微分同胚被$C^r$-由具有简单谱的$C^2$-开集累积。 我们也证明了一类部分双曲映射在最大熵测度下通常是具有简单谱的。 为了证明这些结果，我们给出了一个关于周期点与不变测度同宿相关的Lyapunov谱简单性的准则。 显示英文摘要

摘要： We study the simplicity of the Lyapunov spectrum of partially hyperbolic diffeomorphisms. We prove that a class of volume-preserving partially hyperbolic diffeomorphisms is $C^r$-accumulated by $C^2$-open sets with simple spectrum. Also we prove that a class of partially hyperbolic maps has simple spectrum generically for the measures of maximal entropy. In order to prove these results, we give a criterion for simplicity of the Lyapunov spectrum in terms of periodic points homoclinically related to the invariant measure.