Local and Global Bifurcation for Periodic Solutions of Hamiltonian Systems via Comparison Theory for the Spectral Flow

TL;DR

This paper introduces a novel approach to analyze local and global bifurcations of periodic solutions in Hamiltonian systems using spectral flow comparison theory, highlighting a new method for studying global bifurcation.

Contribution

It applies a comparison principle of spectral flow to establish local and global bifurcation results in Hamiltonian systems, a novel use of spectral flow for global bifurcation analysis.

Findings

Established local bifurcation results for Hamiltonian systems.

First application of spectral flow comparison principle to global bifurcation.

Provided new insights into the structure of periodic solutions.

Abstract

We obtain local and global bifurcation for periodic solutions of Hamiltonian systems by using a new way to apply a comparison principle of the spectral flow that was originally introduced by Pejsachowicz in a joint work with the third author. A particular novelty is the study of global bifurcation, which to the best of our knowledge has not been done via the spectral flow.