2015/08/16 by Thomas Dauer, Dauer, Thomas, Marlies Gerber +1
Mathematics · Physics and Astronomy · #37E99 #78A05 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Primary: 37J99 #Quantum chaos and dynamical systems #Secondary: 53C22 #math.DS #msc:37E99 #msc:37J99 #msc:53C22 #msc:78A05
paper · pdf · doi:10.48550/arxiv.1508.03858
28 pages, 2 figures
arxiv created 2015/08/16 · openalex publication_date 2015/08/16 · arxiv updated 2015/08/18 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Let x and y be points in a billiard table M that is bounded by a curve sigma. We assume that sigma is a simple closed Cr curve with positive curvature, where r is at least 2. A subset B of M\x,y is called a blocking set for the pair (x,y) if every billiard path in M from x to y passes through a point in B. If a finite blocking set exists, the pair (x,y) is called secure in M; if not, it is called insecure. We show that for the generic (in the sense of Baire category) curve sigma, the generic pair of interior points is insecure.