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 language | English (US) |
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Article number | 51 |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 59 |
Issue number | 2 |
DOIs | |
State | Published - 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