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    Homoclinic Points in the Composition of Two Reflections

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    Date
    2013-09-17
    Author
    Jensen, Erik
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    Abstract
    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 $C^1$ functions with domain all of $R$. Let $F:R^2 \to R^2$ denote a horizontal reflection in the curve $x=-f(y)$, and let $G:R^2 \to R^2$ 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 $T$.
    URI for this record
    http://hdl.handle.net/1974/8288
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    • Department of Mathematics and Statistics Graduate Theses
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