迷向流形上同构的同时线性化
Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds
摘要：
设$M$是闭迷向黎曼流形，且$R_1,...,R_m$生成$M$的等距群.设$f_1,...,f_m$是这些等距的光滑扰动。我们证明了$f_i$同时共轭于等距的充要条件是它们的一致Bernoulli随机游动的所有李雅普诺夫指数为零。这将Dolgopyat和Krikorian的线性化结果从$S^n$推广到实、复和四元数射影空间。此外，我们确定并纠正了早期工作中的疏忽。
英文摘要：
Suppose that $M$ is a closed isotropic Riemannian manifold and that $R_1,...,R_m$ generate the isometry group of $M$. Let $f_1,...,f_m$ be smooth perturbations of these isometries. We show that the $f_i$ are simultaneously conjugate to isometries if and only if their associated uniform Bernoulli random walk has all Lyapunov exponents zero. This extends a linearization result of Dolgopyat and Krikorian from $S^n$ to real, complex, and quaternionic projective spaces. In addition, we identify and remedy an oversight in that earlier work.
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