Dynamics of Discontinuous Maps Via Closed Relations

TL;DR

This paper introduces a novel approach to analyze the dynamics of discontinuous maps on compact metric spaces using closed relations, linking it to continuous dynamics on invariant subsets and sample path spaces.

Contribution

It develops a framework connecting discontinuous map dynamics with continuous dynamics via closed relations and invariant G-delta subsets.

Findings

Establishes a method to study discontinuous maps through closed relations.

Connects discontinuous dynamics with continuous dynamics on invariant sets.

Provides insights into the structure of sample path spaces for such systems.

Abstract

For the dynamics of a discontinuous map on a compact metric space, we describe an approach using suitable closed relations and connect it with the continuous dynamics on an invariant G-delta subset and with the continuous dynamics on the compact space of sample paths.