2016/11/22 by José Pedro Gaivão, Gaivão, José Pedro, Serge Troubetzkoy +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1611.07241
openalex publication_date 2016/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new notion of stability for periodic orbits in polygonal\nbilliards. We say that a periodic orbit of a polygonal billiard is\n\λ-stable if there is a periodic orbit for the corresponding pinball\nbilliard which converges to it as \λ \→ 1. This notion of\nstability is unrelated to the notion introduced by Galperin, Stepin and\nVorobets. We give sufficient and necessary conditions for a periodic orbit to\nbe \λ-stable and prove that the set of d-gons having at most finite\nnumber of \λ-stable periodic orbits is dense is the space of d-gons.\nMoreover, we also determine completely the \λ-stable periodic orbits in\nintegrable polygons.\n