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Action and index spectra and periodic orbits in Hamiltonian dynamics. (English) Zbl 1172.53052
The theme of this paper is the interplay between two apects of the dynamics of Hamiltonian systems: the existence of periodic orbits of arbitrary large period, or just of infinitely many periodic orbits, and the behavior of the action or (mean) index spectrum under iterations. Therefore, two main questions are studied: 1) Under what conditions on the manifold and / or the action or index spectrum does a Hamiltonian diffeomorphism have infinitely many (or just many) periodic orbits? 2) What are the special features of the action or index spectrum of a Hamiltonian diffeomorphism with only finitely many periodic orbits?
Let us remark that these two questions, although formally equivalent, represent two very different, virtually opposite perspectives focusing on mutually complementary classes of Hamiltonian diffeomorphisms.

MSC:
53D40 Symplectic aspects of Floer homology and cohomology
37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
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