Dynamical systems with a prescribed attracting set and applications to conservative dynamics

TL;DR

This paper introduces a method to construct dynamical systems with predetermined attracting sets and applies it to create perturbations of conservative systems that have specific leafwise attracting sets.

Contribution

It presents an explicit construction technique for dynamical systems with desired attracting sets and extends this to perturb conservative systems accordingly.

Findings

Constructed dynamical systems with prescribed attracting sets.

Developed a method for perturbing conservative systems to include specific attracting sets.

Provided applications to leafwise attracting sets in conservative dynamics.

Abstract

We provide an explicit method to construct dynamical systems which admit an a-priori prescribed attracting set. As application, we provide a method to construct perturbations of conservative dynamical systems, which admit an a-priori prescribed leafwise attracting set.