Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Generalizations of analogs of theorems of Maizel and Pliss and their application in shadowing theory

Pages: 4187 - 4205, Volume 33, Issue 9, September 2013      doi:10.3934/dcds.2013.33.4187

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Dmitry Todorov - Chebyshev laboratory, Saint Petersburg State University, 14th line of Vasiljevsky Island, 29B, Saint-Petersburg, 199178, Russian Federation (email)

Abstract: We generalize two classical results of Maizel and Pliss that describe relations between hyperbolicity properties of linear system of difference equations and its ability to have a bounded solution for every bounded inhomogeneity. We also apply one of this generalizations in shadowing theory of diffeomorphisms to prove that some sort of limit shadowing is equivalent to structural stability.

Keywords:  Admissibility, difference equations, hyperbolicity, limit shadowing, structural stability.
Mathematics Subject Classification:  Primary: 34D09, 34K12; Secondary: 37C50, 34D30.

Received: February 2012;      Revised: February 2013;      Available Online: March 2013.