Isolating blocks and epsilon chains for maps

Abstract

The relationship between the outputs and computer simulations of dynamical systems and their true orbit structures is explored. Epsilon chains are used as a mathematical representation of computer generated pseudo-orbits. The question "When is a pseudo-orbit shadowed by a true orbit" is discussed. Isolated invariant sets are defined and are shown to be contained in special neighborhoods called isolating blocks. The Conley index is extended and applied to maps. © 1989.