# American Institute of Mathematical Sciences

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Optimizing the stable behavior of parameter-dependent dynamical systems --- maximal domains of attraction, minimal absorption times
June  2014, 1(2): 307-338. doi: 10.3934/jcd.2014.1.307

## 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, Netherlands

Received  July 2013 Revised  December 2013 Published  December 2014

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.
Citation: William D. Kalies, Konstantin Mischaikow, Robert C.A.M. Vandervorst. Lattice structures for attractors I. Journal of Computational Dynamics, 2014, 1 (2) : 307-338. doi: 10.3934/jcd.2014.1.307
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