Applied symbolic dynamics: attractors and filtrations

George Osipenko; Stephen Campbell

doi:10.3934/dcds.1999.5.43

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1999, Volume 5, Issue 1: 43-60. Doi: 10.3934/dcds.1999.5.43

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Applied symbolic dynamics: attractors and filtrations

George Osipenko^1, and
Stephen Campbell²

1.
Laboratory of Nonlinear Analysis and Mathematical Modelling, St.-Petersburg State Technical University, 195251
2.
Department of Mathematics, Belmont University, Nashville, TN

Received: April 30, 1995

Revised: December 31, 1996

Published: December 1998

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Abstract

This paper is a study of the global structure of the attractors of a dynamical system. The dynamical system is associated with an oriented graph called a Symbolic Image of the system. The symbolic image can be considered as a finite discrete approximation of the dynamical system flow. Investigation of the symbolic image provides an opportunity to localize the attractors of the system and to estimate their domains of attraction. A special sequence of symbolic images is considered in order to obtain precise knowledge about the global structure of the attractors and to get filtrations of the system.

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Mathematics Subject Classification: 37B10.

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