Simplicial Dynamical Systems
by
Ethan Akin
City College, CUNY

A simplicial dynamical system is a simplicial map f: K^* --> K, where K^* is a proper subdivision of a simplicial complex K. The dynamical system on the underlying polyhedron obtained by iterating the associated piecewise-linear map can be analyzed completely by using certain subshifts of finite type. Every continuous map on a polyhedron can be uniformly approximated by such a system. This provides a nice view of the computer modeling of the original system. In addition, a number of interesting examples can be constructed using simplicial dynamical systems, e.g. certain space-filling curves and peculiar topological conjugacies.

Date received: June 3, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-40.