Are There Perverse Choreographies?

Alain Chenciner ()
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Alain Chenciner: IMCCE, UMR 8028 du CNRS.77, Astronomie et Systèmes Dynamiques

A chapter in New Advances in Celestial Mechanics and Hamiltonian Systems, 2004, pp 63-76 from Springer

Abstract: 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).

Keywords: Relative Equilibrium; Regular Polygon; Linear Image; Central Configuration; Circular Permutation (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-1-4419-9058-7_4

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