Ergodic Theory and Dynamical Systems

Table of Contents - 01 August 2009 - Volume 29, Issue 04  

Research Article

Embedding diffeomorphisms in flows in Banach spaces

XIANG ZHANGa1

a1 Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, People’s Republic of China (email: xzhang@sjtu.edu.cn)

Abstract

This paper concerns the problem of embedding, in the flow of an autonomous vector field, a local diffeomorphism near a hyperbolic fixed point in a Banach space. To solve the problem, we first extend Floquet theory to Banach spaces, and then prove that two C∞ hyperbolic diffeomorphisms are formally equivalent if and only if they are C∞-equivalent. The latter result is a version, in the Banach space context, of a classical theorem by Chen.

(Received January 31 2008)

(Revised July 29 2008)