Chain recurrence in multidimensional time discrete dynamical systems

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October 2008, 20(4): 1039-1056. doi: 10.3934/dcds.2008.20.1039

Chain recurrence in multidimensional time discrete dynamical systems

1.	Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków

Received March 2007 Revised November 2007 Published January 2008

Abstract
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The author investigates the behavior of multidimensional time discrete dynamical systems. Problems of expansivity, P.O.T.P. and chain recurrence are considered in particular. The main result of this article is a general version of Spectral Decomposition Theorem.

Keywords: chain recurrence, hyperbolicity, spectral decomposition., expansivity, group action, shadowing.

Mathematics Subject Classification: Primary: 37C50; Secondary: 37B0.

Citation: Piotr Oprocha. Chain recurrence in multidimensional time discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 1039-1056. doi: 10.3934/dcds.2008.20.1039

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