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arXiv · 1501.05934

Outer Billiards with Contraction: Attracting Cantor Sets

In-Jee Jeong
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Abstract

We consider the outer billiards map with contraction outside polygons. We construct a 1-parameter family of systems such that each system has an open set in which the dynamics is reduced to that of a piecewise contraction on the interval. Using the theory of rotation numbers, we deduce that every point inside the open set is asymptotic to either a single periodic orbit (rational case) or a Cantor set (irrational case). In particular, we deduce existence of an attracting Cantor set for certain parameter values. Moreover, for a different choice of a 1-parameter family, we prove that the system is uniquely ergodic; in particular, the entire domain is asymptotic to a single attractor.

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In-Jee Jeong. 2015-01-23. Outer Billiards with Contraction: Attracting Cantor Sets. https://arxiv.org/abs/1501.05934

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