### Periodic solutions of a forced relativistic pendulum via twist dynamics

#### Abstract

We prove the existence of at least two geometrically different periodic solutions 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 Poincaré-Birkhoff theorem by Franks. Moreover, with some restriction on the parameters, we prove the existence of twist dynamics.

#### Keywords

Poincaré-Birkhoff fixed point theorem; relative pendulum

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