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Lyapunov maps, simplicial complexes and the Stone functor

Published online by Cambridge University Press:  19 September 2008

Joel W. Robbin  and
Dietmar A. Salamon
Joel W. Robbin
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
Dietmar A. Salamon
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
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Abstract

Let be an attractor network for a dynamical system ft: M → M, indexed by the lower sets of a partially ordered set P. Our main theorem asserts the existence of a Lyapunov map ψ:M → K(P) which defines the attractor network. This result is used to prove the existence of connection matrices for discrete-time dynamical systems.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 1 , March 1992 , pp. 153 - 183
Copyright
Copyright © Cambridge University Press 1992

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