Hamiltonian structures for projectable dynamics on symplectic fiber bundles

Guillermo Dávila-Rascón; Yuri Vorobiev

doi:10.3934/dcds.2013.33.1077

Article Contents

2013, Volume 33, Issue 3: 1077-1088. Doi: 10.3934/dcds.2013.33.1077

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Hamiltonian structures for projectable dynamics on symplectic fiber bundles

Guillermo Dávila-Rascón^1, and
Yuri Vorobiev^1,

1.
Department of Mathematics, University of Sonora, Hermosillo, C.P. 83000

Received: March 31, 2011

Revised: September 30, 2011

Published: February 2013

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Abstract

The Hamiltonization problem for projectable vector fields on general symplectic fiber bundles is studied. Necessary and sufficient conditions for the existence of Hamiltonian structures in the class of compatible symplectic structures are derived in terms of invariant symplectic connections. In the case of a flat symplectic bundle, we show that this criterion leads to the study of the solvability of homological type equations.

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Mathematics Subject Classification: Primary: 53D05, 53D17; Secondary: 70H06, 70H09.

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