We consider a rotating N-centre problem, with N ≥ 3 and homogeneous potentials of degree -α < 0, α ∈ [1,2). We prove the existence of infinitely many collision-free periodic solutions with negative and small Jacobi constant and small values of the angular velocity, for any initial configuration of the centres. We will introduce a Maupertuis' type variational principle in order to apply the broken geodesics technique developed in Soave and Terracini (Discrete Contin Dyn Syst 32:3245-3301, 2012). Major difficulties arise from the fact that, contrary to the classical Jacobi length, the related functional does not come from a Riemaniann structure but from a Finslerian one. Our existence result allows us to characterize the associated dynamical system with a symbolic dynamics, where the symbols are given partitions of the centres in two non-empty sets. © 2013 Springer Basel.

Symbolic dynamics: From the N-centre to the (N + 1)-body problem, a preliminary study

SOAVE, NICOLA
2014

Abstract

We consider a rotating N-centre problem, with N ≥ 3 and homogeneous potentials of degree -α < 0, α ∈ [1,2). We prove the existence of infinitely many collision-free periodic solutions with negative and small Jacobi constant and small values of the angular velocity, for any initial configuration of the centres. We will introduce a Maupertuis' type variational principle in order to apply the broken geodesics technique developed in Soave and Terracini (Discrete Contin Dyn Syst 32:3245-3301, 2012). Major difficulties arise from the fact that, contrary to the classical Jacobi length, the related functional does not come from a Riemaniann structure but from a Finslerian one. Our existence result allows us to characterize the associated dynamical system with a symbolic dynamics, where the symbols are given partitions of the centres in two non-empty sets. © 2013 Springer Basel.
Maupertuis' principle; N-centre problem; Symbolic dynamics; Applied Mathematics; Analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1012886
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