A remark about Sil'nikov saddle-focus homoclinic orbits
Resource
Communications on Pure and Applied Analysis, 10(3), 817-830
Journal
Communications on Pure and Applied Analysis
Pages
817-830
Date Issued
2011
Date
2011
Author(s)
Battelli, Flaviano
Palmer, Kenneth J.
Abstract
In this note we study Sil'nikov saddle-focus homoclinic orbits paying particular attention to four and higher dimensions where two additional conditions are needed. We give equivalent conditions in terms of subspaces associated with the variational equation along the orbit. Then we review Rodriguez'sconstruction of a three-dimensional system with Sil'nikov saddle-focushomoclinic orbits and finally show how to construct higher-dimensional systemswith such orbits.
Type
journal article