Symbolic dynamics for the $N$-centre problem at negative energies

Details Symbolic dynamics for the $N$-centre problem at negative energies Symbolic dynamics for the $N$-centre problem at negative energies

2011-12-31

arxiv.org/abs/1201.0280v1

Mathematics

Dynamical Systems

Scientific paper

We consider the planar $N$-centre problem, with homogeneous potentials of degree $-\a<0$, $\a \in [1,2)$. 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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