We consider the planar N-centre problem, with homogeneous potentials of degree -α < 0, α ε [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.
Symbolic dynamics for the n-centre problem at negative energies
SOAVE, NICOLA;
2012-01-01
Abstract
We consider the planar N-centre problem, with homogeneous potentials of degree -α < 0, α ε [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.File in questo prodotto:
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