Periodic Solutions of a Forced Relativistic Pendulum via Twist Dynamics

Details Periodic Solutions of a Forced Relativistic Pendulum via Twist Dynamics Periodic Solutions of a Forced Relativistic Pendulum via Twist Dynamics

2011-10-04

arxiv.org/abs/1110.0851v1

Mathematics

Dynamical Systems

Scientific paper

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.

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