Introduction

One of the basic tasks in dynamical systems theory is to study structures which persists under small perturbations of the system. As an illustration of this idea, consider the concept of structural stability

Structural stability is an extremely strong demand on a system, since it insists on the persistence of every fine topological detail. Sometimes the study of persistence of much coarser properties is sufficient for the particular application. One of the coarsest of properties is the existence of an attractor , and this is the property under investigation here.

The motivating consideration for this study, and its only application in this paper, is computer simulation of dynamical systems. In a sense, this paper can be viewed as a study of the effect of round-off error on the problem of using direct computer simulations to find attractors of maps.

The numbering of Lemmas, Theorems, Corollaries and Examples follows the numbering of the paper "Some Metric Properties of Attractors with Applications to Computer Simulations of Dynamical Systems" by Richard P. McGehee. You can find a .dvi file here.

Attractors

Attractor blocks

Pseudo-orbits

Intensity

Discrete approximations

Examples

Main entry point