Symbolic dynamics for the N-centre problem at negative energies

2011/12/31 by Nicola Soave, Susanna Terracini, Soave, Nicola +1
Mathematics · #37J30 #37N05 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 70F10 #Secondary: 70F15 #math.DS #msc:37J30 #msc:37N05 #msc:70F10 #msc:70F15

paper · pdf · doi:10.48550/arxiv.1201.0280

arxiv created 2011/12/31 · arxiv updated 2012/01/04

Abstract

We consider the planar N-centre problem, with homogeneous potentials of degree -\a<0, \a ∈ [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the N centres in two non-empty sets.

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