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

Applied symbolic dynamics: attractors and filtrations

Pages: 43 - 60, Volume 5, Issue 1, January 1999      doi:10.3934/dcds.1999.5.43

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George Osipenko - Laboratory of Nonlinear Analysis and Mathematical Modelling, St.-Petersburg State Technical University, 195251, Russian Federation (email)
Stephen Campbell - Department of Mathematics, Belmont University, Nashville, TN, United States (email)

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.

Keywords:  Attractors, symbolic dynamics, discrete dynamical system, homeomorphism.
Mathematics Subject Classification:   37B10.

Received: May 1995;      Revised: January 1997;      Available Online: October 1998.