Periodical Solutions of Multi-Time Hamilton Equations

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dc.creatorUdriste, Constantin
dc.creatorDuca, Iulian
dc.date2005-10-26
dc.date.accessioned2026-07-07T06:47:55Z
dc.date.available2026-07-07T06:47:55Z
dc.descriptionTo 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.
dc.description10 pages Key words: multi-time Hamilton action, periodical extremals, convex Hamiltonian
dc.identifierhttps://arxiv.org/abs/math/0510554
dc.identifierhttp://arxiv.org/abs/math/0510554
dc.identifierAnalele Universitatii Bucuresti, 55, 1 (2005), 179-188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103814
dc.subjectDynamical Systems
dc.subjectAnalysis of PDEs
dc.subject53C21, 49K20, 49S05
dc.titlePeriodical Solutions of Multi-Time Hamilton Equations
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