Some Inequalities Satisfied by Periodical Solutions of Multi-Time Hamilton Equations

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The objective of this paper is to find some inequalities satisfied by periodical solutions of multi-time Hamilton systems, when the Hamiltonian is convex. To our knowledge, this subject of first-order field theory is still open. Section 1 recall well-known facts regarding the equivalence between Euler-Lagrange equations and Hamilton equations and analyses the action that produces multi-time Hamilton equations, emphasizing the role of the polysymplectic structure. Section 2 extends two inequalities of [21] from a cube to parallelipiped and proves two inequalityes concerning multiple periodical solutions of multi-time Hamilton equations.
14 pages, Key words: multi-time Hamilton action, Wirtinger inequality, convex Hamiltonian; Communicated at 5-th Conference of Balkan Society of Geometers (5-th Conference on Differential Geometry), August 28- September 2, 2005, Mangalia, Romania

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Dynamical Systems, Analysis of PDEs, 49S05, 70H05

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http://salesiana.dossiersoluciones.com/handle/123456789/103816

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0510557
 http://arxiv.org/abs/math/0510557

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arXiv