Homoclinic Points in the Composition of Two Reflections

We examine a class of planar area preserving mappings and give a geometric condition that guarantees the existence of homoclinic points. To be more precise, let $f,g:R \to R$ be C¹ functions with domain all of $R$. Let F:R² \to R² denote a horizontal reflection in the curve $x=-f(y)$, and let G:R² \to R² denote a vertical reflection in the curve $y=g(x)$. We consider maps of the form $T=G \circ F$ and show that a simple geometric condition on the fixed point sets of $F$ and $G$ leads to the existence of a homoclinic point for $T$.

Department dc:contributor.department

Mathematics and Statistics

Year dc:date.issued

2013

Author dc:creator

• Jensen, Erik

Advisor dc:contributor.supervisor

• Offin, Daniel

• Area Preserving Maps
• Homoclinic Points
• Mathematics
• Dynamical Systems

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1974/8288

OAI identifier oai:identifier

oai:queensu.scholaris.ca:1974/8288