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VOL. 78 | 2018 Hamiltonian systems on submanifolds
T. Fukuda, S. Janeczko

Editor(s) Shyuichi Izumiya, Goo Ishikawa, Minoru Yamamoto, Kentaro Saji, Takahiro Yamamoto, Masatomo Takahashi

Abstract

A constraint submanifold in a symplectic space after P.A.M. Dirac is determined locally by geometric restriction of the symplectic form to the constraint. The natural symplectic invariant associated to this restriction is the space of Hamiltonian vector fields which uniquely restrict to the solvable Hamiltonian ones on a constraint. By investigation of solvability of generalized Hamiltonian systems we characterize the constraint invariants and find them explicitly in the generic cases. Moreover the Poisson-Lie algebra on submanifold is described and an example of the Hamiltonian vector fields on the 2-sphere in symplectic space was constructed.

Information

Published: 1 January 2018
First available in Project Euclid: 4 October 2018

zbMATH: 1425.53096
MathSciNet: MR3839947

Digital Object Identifier: 10.2969/aspm/07810221

Subjects:
Primary: 51N10, 53D05
Secondary: 15A04, 53D22, 70H05

Rights: Copyright © 2018 Mathematical Society of Japan

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