Connecting Symmetric and Asymmetric Families of Periodic Orbits in Squared Symmetric Hamiltonians

Abstract

In this work, we study a generic squared symmetric Hamiltonian of two degrees of freedom. Our aim is to show a global methodology to analyze the evolution of the families of periodic orbits and their bifurcations. To achieve it, we use several numerical techniques such as a systematic grid search algorithm in sequential and parallel, a fast chaos indicator and a tool for the continuation of periodic orbits. Using them, we are able to study the special and generic bifurcations of multiplicity one that allow us to understand the dynamics of the system and we show in detail the evolution of some symmetric breaking periodic orbits.

New developments in classical chaotic scattering

“…On the other hand, this system has been the focus in the last few years as a prototype model to study bifurcations and chaos in Hamiltonian systems [153]. This kind of analysis has also been carried out by Blesa et al in [154]. Besides, a thorough study of the fractal structures in the phase space of this system has been carried out in [155,156].…”