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Are There Perverse Choreographies?

In: New Advances in Celestial Mechanics and Hamiltonian Systems

Author

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  • Alain Chenciner

    (IMCCE, UMR 8028 du CNRS.77, Astronomie et Systèmes Dynamiques
    Université Paris VII-Denis Diderot 16, Departement de Mathématiques)

Abstract

Let C(t = (q(t+1), q(t+2), ⋯, q(t+n) = q(t))be a planar choreography of period n of the n punctual masses m1, m2,…mn, that is a planar n-periodic solution of the n-body problem where all n bodies follow one and the same curve qit) with equal time spacing (see [2]). In the sequel, we shall identify the planar curve q(t) with a mapping q: ℝ/nℤ → ℂ (for convenience of notation, we have chosen the period to be n; well chosen homotheties on configuration and velocities reduce the general case to this one).

Suggested Citation

  • Alain Chenciner, 2004. "Are There Perverse Choreographies?," Springer Books, in: J. Delgado & E. A. Lacomba & J. Llibre & E. Pérez-Chavela (ed.), New Advances in Celestial Mechanics and Hamiltonian Systems, pages 63-76, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9058-7_4
    DOI: 10.1007/978-1-4419-9058-7_4
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