Lin's method for heteroclinic chains involving periodic orbits

TL;DR

This paper extends Lin's method to analyze heteroclinic chains connecting equilibria and periodic orbits, providing a framework for understanding bifurcations near complex cycle structures in dynamical systems.

Contribution

The paper introduces a novel extension of Lin's method tailored for heteroclinic chains involving both equilibria and periodic orbits, with new estimates for jump conditions.

Findings

Derived jump estimates for Lin orbits

Bifurcation equations for homoclinic orbits near EtoP cycles

Framework for analyzing heteroclinic chain bifurcations

Abstract

We present an extension of the theory known as Lin's method to heteroclinic chains that connect hyperbolic equilibria and hyperbolic periodic orbits. Based on the construction of a so-called Lin orbit, that is, a sequence of continuous partial orbits that only have jumps in a certain prescribed linear subspace, estimates for these jumps are derived. We use the jump estimates to discuss bifurcation equations for homoclinic orbits near heteroclinic cycles between an equilibrium and a periodic orbit (EtoP cycles).