NORMALIZATION OF THE HAMILTONIAN AND THE ACTION SPECTRUM

Title & Authors
NORMALIZATION OF THE HAMILTONIAN AND THE ACTION SPECTRUM
OH YONG-GEUN;

Abstract
In this paper, we prove that the two well-known natural normalizations of Hamiltonian functions on the symplectic manifold ($\small{M,\;{\omega}}$) canonically relate the action spectra of different normalized Hamiltonians on arbitrary symplectic manifolds ($\small{M,\;{\omega}}$). The natural classes of normalized Hamiltonians consist of those whose mean value is zero for the closed manifold, and those which are compactly supported in IntM for the open manifold. We also study the effect of the action spectrum under the $\small{{\pi}_1}$ of Hamiltonian diffeomorphism group. This forms a foundational basis for our study of spectral invariants of the Hamiltonian diffeomorphism in [8].
Keywords
Hamiltonians;normalization;action functional;action spectrum;
Language
English
Cited by
1.
FLOER MINI-MAX THEORY, THE CERF DIAGRAM, AND THE SPECTRAL INVARIANTS,;

대한수학회지, 2009. vol.46. 2, pp.363-447
1.
CONTINUOUS HAMILTONIAN DYNAMICS AND AREA-PRESERVING HOMEOMORPHISM GROUP OF D2, Journal of the Korean Mathematical Society, 2016, 53, 4, 795
2.
Calabi quasi-morphisms for some non-monotone symplectic manifolds, Algebraic & Geometric Topology, 2006, 6, 1, 405
3.
Hamiltonian Floer homology for compact convex symplectic manifolds, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016, 57, 2, 361
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