Conjugate points on geodesics of Hofer's metric
Hofer's metric on the group of Hamiltonian diffeomorphisms of a symplectic manifold is generated by the \(L^\infty\)-norm on the Lie algebra. In this paper we develop a variational theory of geodesics of this metric which satisfy certain non-degeneracy assumptions. We derive the second variation formula, describe conjugate points and obtain necessary and sufficient conditions for the \(C^\infty\)-local minimality of such geodesics. We also present an example of a nondegenerate geodesic which is not locally minimal at its first conjugate point.
scientific article; zbMATH DE number 937462