Chaotic behaviour and symbolic dynamics in Celestial Mechanics

Abstract: We consider the planar N-centre problem, with homogeneous potentials of negative degree, possibly anisotropic. 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.

Mathematics

Audience: researchers in the discipline

Barcelona Mathematical Days 2020

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