Double flip bifurcations in $\mathbb{Z}/2\mathbb{Z}$-symmetric Hamiltonian systems

TL;DR

This paper introduces the double flip bifurcation in $\

Contribution

It presents the concept of double flip bifurcation in Hamiltonian systems and derives a normal form for systems undergoing this bifurcation.

Findings

Normal form for double flip bifurcation derived

Double flip bifurcation involves two simultaneous Hamiltonian flip bifurcations

Connected by a curve of singular points

Abstract

In this paper we introduce a new bifurcation in Hamiltonian systems, which we call the double flip bifurcation. The Hamiltonian depends on two parameters, one of which controls the double flip bifurcation. The result of the bifurcation is the occurrence of two Hamiltonian flip bifurcations with respect to the other parameter. The two Hamiltonian flip bifurcations are simultaneous with respect to the first parameter, and are connected by a curve-segment of singular points. We find a normal form for Hamiltonians describing systems going through double flip bifurcations, and compute said normal form for some examples.