# Twist dynamics and Aubry-Mather sets around a periodically perturbed point-vortex

## TL;DR

This paper investigates the dynamics of a point-vortex system under periodic perturbations, establishing conditions for quasi-periodic solutions using Aubry-Mather theory to analyze minimal orbits.

## Contribution

It introduces sufficient conditions for the existence of quasi-periodic solutions in a periodically perturbed point-vortex model, applying Aubry-Mather theory to this context.

## Key findings

- Existence of generalized quasi-periodic solutions with specific rotation numbers.
- Identification of minimal orbits of the Poincaré map in the perturbed vortex system.
- Application of Aubry-Mather theory to vortex dynamics under periodic forcing.

## Abstract

We consider the model of a point-vortex under a periodic perturbation and give sufficient conditions for the existence of generalized quasi-periodic solutions with rotation number. The proof uses Aubry-Mather theory to obtain the existence of a family of minimal orbits of the Poincar\'e map associated to the system.