2014/02/10 by Zijian Yao, Yao, Zijian
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.1402.2319
15 pages, 12 figures
arxiv created 2014/02/10 · openalex publication_date 2014/02/10 · arxiv updated 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
In this paper, we discuss rotation number on the invariant curve of a one parameter family of outer billiard tables. Given a convex polygon η, we can construct an outer billiard table T by cutting out a fixed area from the interior of η. T is piece-wise hyperbolic and the polygon η is an invariant curve of T under the billiard map ϕ. We will show that, if β is a periodic point under the outer billiard map with rational rotation number τ= p / q, then the nth iteration of the billiard map is not the local identity at β. This proves that the rotation number τ as a function of the area parameter is a devil's staircase function.