Ergodic Theory and Dynamical Systems

Research Article

Lyapunov maps, simplicial complexes and the Stone functor

Joel W. Robbina1 and Dietmar A. Salamona2

a1 Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

a2 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK

Abstract

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

(Received November 27 1990)