Lin's method for heteroclinic chains involving periodic orbits
Dynamical Systems
2015-05-13 v1
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).
Cite
@article{arxiv.0903.4902,
title = {Lin's method for heteroclinic chains involving periodic orbits},
author = {Jürgen Knobloch and Thorsten Rieß},
journal= {arXiv preprint arXiv:0903.4902},
year = {2015}
}