American Institute of Mathematical Sciences

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January  1999, 5(1): 43-60. doi: 10.3934/dcds.1999.5.43

Applied symbolic dynamics: attractors and filtrations

George Osipenko 1, and  Stephen Campbell 2,

1. 

Laboratory of Nonlinear Analysis and Mathematical Modelling, St.-Petersburg State Technical University, 195251, Russian Federation
2. 

Department of Mathematics, Belmont University, Nashville, TN, United States

Received  May 1995 Revised  January 1997 Published  October 1998

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: homeomorphism., symbolic dynamics, Attractors, discrete dynamical system.
Mathematics Subject Classification: 37B1.
Citation: George Osipenko, Stephen Campbell. Applied symbolic dynamics: attractors and filtrations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 43-60. doi: 10.3934/dcds.1999.5.43
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