Periodic Solutions of a Forced Relativistic Pendulum via Twist Dynamics

TL;DR

This paper proves the existence of multiple periodic solutions and twist dynamics in a forced relativistic pendulum, using topological methods and the Poincaré-Birkhoff theorem, and also analyzes solution stability.

Contribution

It introduces a topological approach to establish multiple periodic solutions and twist dynamics in the relativistic pendulum model, extending previous results.

Findings

Existence of at least two distinct periodic solutions with winding number N.

Proof of solution instability under certain conditions.

Conditions under which twist dynamics occur.

Abstract

We prove the existence of at least two geometrically different periodic solution with winding number N for the forced relativistic pendulum. The instability of a solution is also proved. The proof is topological and based on the version of the Poincar\'e-Birkhoff theorem by Franks. Moreover, with some restriction on the parameters, we prove the existence of twist dynamics.