Some Inequalities Satisfied by Periodical Solutions of Multi-Time Hamilton Equations
arXiv:math/0510557
Abstract
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