Characterization of hyperbolicity and generalized shadowing lemma
Dynamical Systems
2011-07-19 v1
Abstract
J. Mather characterized uniform hyperbolicity of a discrete dynamical system as equivalent to invertibility of an operator on the set of all sequences bounded in norm in the tangent bundle of an orbit. We develop a similar characterization of nonuniform hyperbolicity and show that it is equivalent to invertibility of the same operator on a larger, Fr\'echet space. We apply it to obtain a condition for a diffeomorphism on the boundary of the set of Anosov diffeomorphisms to be nonuniformly hyperbolic. Finally we generalise the Shadowing lemma in the same context.
Cite
@article{arxiv.1107.3216,
title = {Characterization of hyperbolicity and generalized shadowing lemma},
author = {Davor Dragicevic and Sinisa Slijepcevic},
journal= {arXiv preprint arXiv:1107.3216},
year = {2011}
}