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Embedding diffeomorphisms in flows in Banach spaces

Published online by Cambridge University Press:  01 August 2009

XIANG ZHANG
XIANG ZHANG*
Affiliation:
Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, People’s Republic of China (email: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 4 , August 2009 , pp. 1349 - 1367
Copyright
Copyright © Cambridge University Press 2009

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