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We show that whenever a Hamiltonian diffeomorphism or a Reeb flow has afinite number of periodic orbits, the mean indices of these orbits must satisfya resonance relation, provided that the ambient manifold meets some naturalrequirements. In the case of Reeb flows, this leads to simple expressions(purely in terms of the mean indices) for the mean Euler characteristics. Theseare invariants of the underlying contact structure which are capable ofdistinguishing some contact structures that are homotopic but notdiffeomorphic.

Homological Resonances for Hamiltonian Diffeomorphisms and Reeb Flows