A K-theoretical Invariant and Bifurcation for Homoclinics of Hamiltonian Systems

TL;DR

This paper applies a K-theoretical invariant to study bifurcations of homoclinic solutions in families of Hamiltonian systems parametrized by tori, offering new insights into their bifurcation structure.

Contribution

It introduces a novel application of a K-theoretical invariant to analyze bifurcations of homoclinic solutions in Hamiltonian systems parametrized by tori.

Findings

Identification of bifurcation points for homoclinic solutions

Extension of K-theoretical methods to Hamiltonian systems

New criteria for bifurcation detection in multiparameter settings

Abstract

We revisit a K-theoretical invariant that was invented by the first author some years ago for studying multiparameter bifurcation of branches of critical points of functionals. Our main aim is to apply this invariant to investigate bifurcation of homoclinic solutions of families of Hamiltonian systems which are parametrised by tori.