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

@article{Hu2020ADB,
  title={A dihedral Bott-type iteration formula and stability of symmetric periodic orbits},
  author={Xijun Hu and Alessandro Portaluri and Ran Yang},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2020},
  volume={59},
  pages={1-40}
}
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. 
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