Bifurcations of balanced configurations for the Newtonian n-body problem in R4

Luca Asselle, Marco Fenucci, Alessandro Portaluri

Research output: Contribution to journalArticlepeer-review

Abstract

For the gravitational n-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration featuring suitable properties. While in dimension d≤ 3 the configuration must be central, in dimension d≥ 4 new possibilities arise due to the complexity of the orthogonal group, and indeed there is a wider class of S-balanced configurations, containing central ones, which yield simple solutions of the n-body problem. Starting from the recent results in [2], we study the existence of continua of bifurcations branching from a trivial branch of collinear S-balanced configurations and provide an estimate from below on the number of bifurcation instants. In the last part of the paper, by using the continuation method, we explicitly display the bifurcation branches in the case of the three body problem for different choices of the masses.

Original languageEnglish (US)
Article number22
JournalJournal of Fixed Point Theory and Applications
Volume24
Issue number2
DOIs
StatePublished - Jun 2022

Keywords

  • balanced configurations
  • bifurcation of critical points
  • central configurations
  • n-Body problem
  • spectral flow of symmetric matrices

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics

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