# Chaos in periodically forced reversible vector fields

## TL;DR

This paper investigates how periodic forcing of reversible vector fields in the plane can induce chaos, characterized by topological horseshoes, using normal forms and classification of reversible vector fields.

## Contribution

It introduces a method to generate chaos in reversible vector fields through periodic forcing, expanding understanding of chaotic dynamics in symmetric systems.

## Key findings

- Periodic forcing can induce topological chaos in reversible vector fields.
- Normal forms help classify and analyze chaotic behavior.
- Chaos is demonstrated via semi-conjugacy to a shift in a finite alphabet.

## Abstract

We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of pulse form may be added to them to yield topological chaotic behaviour. Chaos here means that the resulting dynamics is semi-conjugate to a shift in a finite alphabet. The results rely on the classification of reversible vector fields and on the theory of topological horseshoes. This work is part of a project of studying periodic forcing of symmetric vector fields.