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Title: Hamiltonian structures of the first variation equations and symplectic connections

Abstract

Necessary and sufficient conditions in terms of symplectic connections, ensuring that the first variation equation of a Hamiltonian system along a fixed invariant symplectic submanifold is also a Hamiltonian system with respect to some admissible symplectic structure are obtained. The class of admissible symplectic structures is distinguished by means of the natural condition of compatibility with the symplectic 2-form in the ambient space. Possible obstructions to the existence of a Hamiltonian structure on the first variation equation are investigated.

Authors:
 [1]
  1. Moscow State Institute of Electronics and Mathematics - Technical University, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
21202923
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 191; Journal Issue: 4; Other Information: DOI: 10.1070/SM2000v191n04ABEH000468; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPATIBILITY; EQUATIONS; HAMILTONIANS; MATHEMATICAL SPACE; VARIATIONS

Citation Formats

Vorob'ev, Yu M. Hamiltonian structures of the first variation equations and symplectic connections. United States: N. p., 2000. Web. doi:10.1070/SM2000V191N04ABEH000468; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Vorob'ev, Yu M. Hamiltonian structures of the first variation equations and symplectic connections. United States. doi:10.1070/SM2000V191N04ABEH000468; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Vorob'ev, Yu M. Sun . "Hamiltonian structures of the first variation equations and symplectic connections". United States. doi:10.1070/SM2000V191N04ABEH000468; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21202923,
title = {Hamiltonian structures of the first variation equations and symplectic connections},
author = {Vorob'ev, Yu M},
abstractNote = {Necessary and sufficient conditions in terms of symplectic connections, ensuring that the first variation equation of a Hamiltonian system along a fixed invariant symplectic submanifold is also a Hamiltonian system with respect to some admissible symplectic structure are obtained. The class of admissible symplectic structures is distinguished by means of the natural condition of compatibility with the symplectic 2-form in the ambient space. Possible obstructions to the existence of a Hamiltonian structure on the first variation equation are investigated.},
doi = {10.1070/SM2000V191N04ABEH000468; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 4,
volume = 191,
place = {United States},
year = {2000},
month = {4}
}