2015/01/23 by In-Jee Jeong, In‐Jee Jeong, Jeong, In-Jee
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.1501.05934
20 pages
arxiv created 2015/01/23 · openalex publication_date 2015/01/23 · arxiv updated 2015/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.