Lattice structures for attractors  I

William D. Kalies; Konstantin Mischaikow; Robert C.A.M. Vandervorst

doi:10.3934/jcd.2014.1.307

Article Contents

2014, Volume 1, Issue 2: 307-338. Doi: 10.3934/jcd.2014.1.307

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Lattice structures for attractors I

1.
Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, 33431 Boca Raton
2.
Rutgers University, 110 Frelinghusen Road, Piscataway, NJ 08854
3.
VU University, De Boelelaan 1081a, 1081 HV, Amsterdam

Received: June 30, 2013

Revised: November 30, 2013

Published: May 2014

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Abstract

We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and noninvertible. We separate those properties which rely solely on algebraic structures from those that require some topological arguments, in order to lay a foundation for the development of algorithms to manipulate these structures computationally.

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Mathematics Subject Classification: Primary: 37B25, 06D05; Secondary: 37B35.

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