# ($\varepsilon$, T )-Chains and Chain Recurrence in Graph Determined Hybrid Dynamical Systems

## TL;DR

This paper extends discrete dynamical systems to continuous time, analyzing limit behavior and recurrence in a skew product flow involving Euclidean space, and introduces new concepts for these systems.

## Contribution

It develops a continuous time extension of discrete systems and studies recurrence and limit behaviors in this new framework, including skew product flows.

## Key findings

- Analysis of limit behavior in continuous time systems
- Recurrence properties in skew product flows
- Behavioral insights on Euclidean space components

## Abstract

This paper examines a continuous time dynamical system that is an extension of a discrete time dynamical system previously examined, and considers this system together in a product space with a compact subset of Euclidean space. Together, the two systems give a skew product flow. We first examine limit behavior and recurrence in our continuous time extension. We then consider analogous limit and recurrence concepts for a skew product flow, and the behavior on the Euclidean space that results.