An "n" Center Problem as an Example of a Geodesic Billiard Map with Singularities: Poincaré Maps and Dynamics

• Antonio García ^[1]
  1. [1] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 14, Nº 2, 2015 (Ejemplar dedicado a: Hamiltonian Systems and Celestial Mechanics, HAMSYS-2014), págs. 209-225
• Idioma: inglés
• DOI: 10.1007/s12346-015-0165-9
• Texto completo no disponible (Saber más ...)
• Resumen

  • This paper deals with the motion of a particle of infinitesimal mass and moving under the gravitational attraction of n particles of equal mass and fixed in the vertices of a regular polygon. The complete reduction of this problem is done using its finite group of symmetries. We show that it is the lift of a flow which is topologically conjugate to a geodesic billiard problem with the Jacobi metric and also study numerically the corresponding billiard maps.