论文标题
各向同性歧管的差异性的同时线性化
Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds
论文作者
论文摘要
假设$ m $是封闭的各向同性Riemannian歧管，而$ r_1，...，r_m $生成$ m $的等轴测组。令$ f_1，...，f_m $是这些异构体的平滑扰动。我们证明，$ f_i $在且仅当其相关统一的bernoulli随机步行中，同时是与等法的共轭。这将Dolgopyat和Krikorian的线性化结果从$ s^n $扩展到了真实，复杂和Quaternionic投射空间。此外，我们在早期工作中确定并纠正了监督。
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.
