On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere

  1. León, Miguel A. González 1
  2. Guilarte, Juan Mateos
  3. Mayado, Marina de la Torre 1
  1. 1 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

Book:
Integrability, Supersymmetry and Coherent States

ISBN: 978-3-030-20087-9 978-3-030-20086-2

Year of publication: 2019

Pages: 359-373

Type: Book chapter

DOI: 10.1007/978-3-030-20087-9_16 GOOGLE SCHOLAR lock_openOpen access editor

Sustainable development goals

Abstract

Separable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context.

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