Periodical Solutions of Multi-Time Hamilton Equations

Abstract

To our knowledge, there are two main references [9], [12] regarding the periodical solutions of multi-time Euler-Lagrange systems, even if the multi-time equations appeared in 1935, being introduced by de Donder. That is why, the central objective of this paper is to solve an open problem raised in [12]: what we can say about periodical solutions of multi-time Hamilton systems when the Hamiltonian is convex? Section 1 recall well-known facts regarding the equivalence between Euler-Lagrange equations and Hamilton equations. Section 2 analyzes the action that produces multi-time Hamilton equations, and introduces the Legendre transform of a Hamiltonian together a new dual action. Section 3 proves the existence of periodical solutions of multi-time Hamilton equations via periodical extremals of the dual action, when the Hamiltonian is convex.

10 pages Key words: multi-time Hamilton action, periodical extremals, convex Hamiltonian

References in corpus (1)

• From PDE Systems and Metrics to Generalized Field Theories

Cited by in corpus (5)

• Fractional Action-Like Variational Problems
• Some Inequalities Satisfied by Periodical Solutions of Multi-Time Hamilton Equations
• Poisson-Gradient Dynamical Systems with Convex Potential
• Periodical Solutions of Poisson-Gradient Dynamical Systems with Periodical Potential
• Poisson-Gradient Dynamical Systems with Bounded Non-Linearity