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.
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