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 2005 |
Keywords
- Chaos
- Newton's method
- Pseudo orbits
- Shadowing
- Transversal homoclinic orbits
ASJC Scopus subject areas
- Analysis