Normalization of the Hamiltonian and the action spectrum

Abstract

In this paper, we prove that the two well-known natural normalizations of Hamiltonian functions on the symplectic manifold $(M,\omega )$ canonically relates the action spectra of different normalized Hamiltonians on {\it arbitrary} symplectic manifolds $(M,\omega )$. The natural class of normalized Hamiltonians consists of those whose mean value is zero for the closed manifold, and those which are compactly supported in $\text{Int}M$ for the open manifold. We also study the effect of the action spectrum under the ${\pi }_1$ of Hamiltonian diffeomorphism group. This forms a foundational basis for our study of spectral invariants of the Hamiltonian diffeomorphism in [Oh4].

15 pages, typos corrected

References in corpus (1)

• Mini-max theory, spectral invariants and geometry of the Hamiltonian diffeomorphism group