A dihedral Bott-type iteration formula and stability of symmetric periodic orbits

Xijun Hu, Alessandro Portaluri, Ran Yang

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by the recent discoveries on the stability properties of symmetric periodic solutions of Hamiltonian systems, we establish a Bott-type iteration formula for dihedraly equivariant Hamiltonian systems. We apply the abstract theory for computing the Morse indices of the celebrated Chenciner and Montgomery figure-eight orbit for the planar three body problem in different equivariant spaces. Finally we provide a hyperbolicity criterion for reversible Lagrangian systems.

Original languageEnglish (US)
Article number51
JournalCalculus of Variations and Partial Differential Equations
Volume59
Issue number2
DOIs
StatePublished - Apr 1 2020

Keywords

  • 3-Body problem
  • Bott iteration formula
  • Equivariant dihedral group action
  • Linear stability
  • Maslov index
  • Spectral flow

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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