2007/05/07 by Mário Carneiro, Carneiro, M. J. Dias, Sylvie Oliffson Kamphorst +3
Mathematics · Physics and Astronomy · #37C20 #37E40 #Advanced Differential Equations and Dynamical Systems #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.0705.0948
openalex publication_date 2007/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period, all non-degenerate and at least one of them is hyperbolic. Moreover, the invariant curves of two hyperbolic points are transversal. We explore these properties to give some dynamical consequences specially about the dynamics in the instability regions.