2011/08/04 by Victoria Blumen, Ki Yeun Kim, Blumen, Victoria +5
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.1108.0987
openalex publication_date 2011/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on hyperbolic plane, as in the planar case, has zero measure. For the sphere, a new proof of Baryshnikov's theorem is obtained which states that 3-period orbits can form a set of positive measure provided a natural condition on the orbit length is satisfied.