Finite Precision Approximation of Dynamical Systems
by
Fern Y. Hunt
National Institute of Standards and Technology

Given a finite dimensional map T of a compact space X to itself, we study the Markov chain approximation of T based on a partition of X. The sample paths are epsilon chains and when the map is continuous approximations to chain transitive sets, and attractors that are stable to perturbations can be constructed in terms of the communication classes of the Markov chain. If an attractor is the support of a BRS measure then the chain is irrreducible and there is a unique stationary state of the chain. If the attractor is transitive as well as asymptotically stable, the stationary state is an approximation of this measure in the limit as the partition diameter tends to zero.

Date received: February 13, 1998