Abstract
A new method for rigorously establishing the existence of a transversal homoclinic orbit to a periodic orbit (or a fixed point) of diffeomorphisms in R n is presented. It is a computer-assisted technique with two main components. First, a global Newton's method is devised to compute a suitable pseudo (approximate) homoclinic orbit to a pseudo periodic orbit. Then, a homoclinic shadowing theorem, which is proved herein, is invoked to establish the existence of a true transversal homoclinic orbit to a true periodic orbit near these pseudo orbits.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 175-215 |
| Number of pages | 41 |
| Journal | Journal of Dynamics and Differential Equations |
| Volume | 17 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2005 |
Keywords
- Chaos
- Newton's method
- Pseudo orbits
- Shadowing
- Transversal homoclinic orbits
ASJC Scopus subject areas
- Analysis
Fingerprint Dive into the research topics of 'Homoclinic shadowing'. Together they form a unique fingerprint.
Cite this
Coomes, B. A., Koçak, H., & Palmer, K. J. (2005). Homoclinic shadowing. Journal of Dynamics and Differential Equations, 17(1), 175-215. https://doi.org/10.1007/s10884-005-3146-x