A Shadowing Lemma with Applications to Semilinear Parabolic Equations
- 1 May 1989
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 20 (3) , 547-557
- https://doi.org/10.1137/0520038
Abstract
The property of hyperbolic sets that is embodied in the Shadowing Lemma is of great importance in the theory of dynamical systems. In this paper a new proof of the lemma is presented, which applies not only to the usual case of a diffeomorphism in finite-dimensional space but also to a sequence of possibly noninvertible maps in a Banach space. The approach is via Newton’s method, the main step being the verification that a certain linear operator is invertible. At the end of the paper an application to parabolic evolution equations is given.Keywords
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