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
2014-01-01
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.File | Dimensione | Formato | |
---|---|---|---|
Symbolic dynamics-from the N-centre_11311-1012886_Soave.pdf
accesso aperto
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
930.37 kB
Formato
Adobe PDF
|
930.37 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.