| | |
Summary: Periodic Solutions of a Forced
Relativistic Pendulum via Twist
Dynamics
Stefano Mar`o
Dipartimento di Matematica - Universit`a di Torino
Via Carlo Alberto 10, 10123 Torino - Italy
e-mail: stefano.maro@unito.it
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 ex-
istence of twist dynamics.
1 Introduction and statement of the main re-
sults
We are concerned with the equation of the forced relativistic pendulum
(1)
d
dt
|
