PARTIALLY HYPERBOLIC DYNAMICS IN DIMENSION THREE

三维空间中的部分双曲动力系统

单超

11930566

硕士

数学

Raul Ures

2021-05-20

2021-05-20

南方科技大学

深圳

Pugh and Shub have conjectured that the abundance of stable ergodicity among conservative partially hyperbolic diffeomorphisms. Based on the notion of accessibility, theypropose a program to prove their conjecture and split it into two parts. The first step isto prove that accessibility will imply ergodicity, then in the second step they claim thataccessibility is in fact 𝐶1open and 𝐶∞ dense among conservative partially hyperbolicdiffeomorphisms. We will use a more tidy language to narrate and reorganize the proof ofthe second step of conjecture in dimension three (or for one dimensional center bundle).

Pugh 和 Shub 猜想稳定遍历微分同胚系统在保守的部分双曲微分同胚系统中是稠密的。他们基于可达性把这个猜想分为两个步骤，首先先证明可达性是蕴含着遍历性的，其次再证明可达性在保守的部分双曲微分同胚系统中是 𝐶1 开的和 𝐶∞稠密的。本文将用更简洁的语言叙述并整理在流形是三维（或者中心丛是一维）的情况下第二个步骤的证明。

partially hyperbolic Pugh-Shub conjecture accessibility ergodicity dense

Pugh-Shub 猜想 部分双曲微分集 可达性 遍历性 稠密性

英语

独立培养

南方科技大学

Dan C. PARTIALLY HYPERBOLIC DYNAMICS IN DIMENSION THREE[D]. 深圳. 南方科技大学,2021.