High-Precision Continuation of Periodic Orbits

Abstract EN

Obtaining periodic orbits of dynamical systems is the main source of information about how the orbits, in general, are organized.

In this paper, we extend classical continuation algorithms in order to be able to obtain families of periodic orbits with high-precision.

These periodic orbits can be corrected to get them with arbitrary precision.

We illustrate the method with two important classical Hamiltonian problems.