Experimental Mathematics

Forcing Relations for Homoclinic Orbits of the Smale Horseshoe Map

Pieter Collins

Full-text: Open access

Abstract

An important problem in the dynamics of surface homeomorphisms is determining the forcing relation between orbits. The forcing relation between periodic orbits can be computed using existing algorithms. Here we consider forcing relations between homoclinic orbits. We outline a general procedure for computing the forcing relation and apply this to compute the equivalence and forcing relations for homoclinic orbits of the Smale horseshoe map.

Article information

Source
Experiment. Math., Volume 14, Issue 1 (2005), 75-86.

Dates
First available in Project Euclid: 30 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.em/1120145572

Mathematical Reviews number (MathSciNet)
MR2146521

Zentralblatt MATH identifier
1107.37031

Subjects
Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 37C27: Periodic orbits of vector fields and flows 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx] 37E25: Maps of trees and graphs

Keywords
Homoclinic orbit forcing relation Smale horseshoe braid type

Citation

Collins, Pieter. Forcing Relations for Homoclinic Orbits of the Smale Horseshoe Map. Experiment. Math. 14 (2005), no. 1, 75--86. https://projecteuclid.org/euclid.em/1120145572


Export citation