Spectral flow and bifurcation of critical points of strongly indefinite functionals. II: Bifurcation of periodic orbits of Hamiltonian systems
Part I, cf. J. Funct. Anal. 162, 52-95 (1999; Zbl 0915.58091). The paper deals with the bifurcation of periodic orbits for time dependent Hamiltonian systems. First the authors study the bifurcation of periodic orbits from equilibrium points under the assumption that the linearization along the trivial branch is induced by a time independent Hamiltonian. Hence the spectral flow of the path of Hessians of the associated action functionals reduces to the difference of generalized signatures of the Hessians at the ends of the path. The authors show that the index of a linear Hamiltonian system introduced by Amann and Zehnder that was used to find multiple solutions of a Hamiltonian system can also be used in order to detect bifurcation for the problems under consideration. Moreover, they present a very simple and explicit calculation of the spectral flow in the particular case when the Hessians of the Hamiltonians commute with the symplectic matrix. The authors consider the general case of bifurcation of periodic orbits (with fixed period) from a known branch of periodic solutions, too.
scientific article; zbMATH DE number 1454724
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