Chaotic orbits for systems of nonlocal equations

TL;DR

This paper explores chaotic and complex trajectories in nonlocal systems driven by periodic potentials, introducing a variational approach to fractional dynamical systems and establishing symbolic dynamics results.

Contribution

It is the first to analyze nonlocal dynamical systems in a variational framework and to demonstrate symbolic dynamics in a fractional setting.

Findings

Constructed multibump solutions connecting integer points.

Established existence of heteroclinic, homoclinic, and chaotic trajectories.

First to analyze nonlocal systems with symbolic dynamics in a variational approach.

Abstract

We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic trajectories are constructed. This is the first attempt to consider a nonlocal version of this type of dynamical systems in a variational setting and the first result regarding symbolic dynamics in a fractional framework.