A finite-time condition for exponential dichotomy
Resource
Journal of Difference Equations and Applications, 17(2), 221-234
Journal
The Journal of Difference Equations and Applications
Pages
221-234
Date Issued
2011
Date
2011
Author(s)
Palmer, Kenneth J.
Abstract
We prove that if a difference equation on Z has an exponential dichotomy on sufficiently many intervals of sufficiently large fixed length and with uniform constants and exponents, then it has an exponential dichotomy on Z. We give applications of the result to slowly varying systems, almost periodic systems, a perturbation theorem, the variational equation along pseudo orbits lying in a hyperbolic set of a diffeomorphism, transversality of homoclinic orbits of a diffeomorphism and hyperbolicity of a compact invariant set of a diffeomorphism.
Type
journal article
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