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).
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References
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Chenciner, A. (2004). Are There Perverse Choreographies?. In: Delgado, J., Lacomba, E.A., Llibre, J., Pérez-Chavela, E. (eds) New Advances in Celestial Mechanics and Hamiltonian Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9058-7_4
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DOI: https://doi.org/10.1007/978-1-4419-9058-7_4
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