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

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

2005-10-26

arxiv.org/abs/math/0510557v1

Mathematics

Dynamical Systems

14 pages, Key words: multi-time Hamilton action, Wirtinger inequality, convex Hamiltonian; Communicated at 5-th Conference of

Scientific paper

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.

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