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 Poincar´e-Birkhoff theorem by Franks. Moreover, with some restriction on the parameters, we prove the existence of twist dynamics.
Periodic solutions of a forced relativistic pendulum via twist dynamics
MARO', STEFANO
2013-01-01
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 Poincar´e-Birkhoff theorem by Franks. Moreover, with some restriction on the parameters, we prove the existence of twist dynamics.
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