Admissibility, a  general type of Lipschitz shadowing and structural stability

Davor Dragičević

doi:10.3934/cpaa.2015.14.861

Article Contents

2015, Volume 14, Issue 3: 861-880. Doi: 10.3934/cpaa.2015.14.861

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Admissibility, a general type of Lipschitz shadowing and structural stability

Davor Dragičević^1,

1.
Department of Mathematics, University of Rijeka, 51000 Rijeka

Received: April 30, 2014

Revised: September 30, 2014

Published: April 2015

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Abstract

For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of a uniform exponential dichotomy and we characterize it completely in terms of the admissibility of a large class of function spaces. We apply those results to show that structural stability of a diffeomorphism is equivalent to a very general type of Lipschitz shadowing property. Our results extend those in [37] in various directions.

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Mathematics Subject Classification: Primary: 34D09, 34K12; Secondary: 37C50, 37D20.

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