Frontiers of Mathematics in China >

2008 , Vol. 3 >Issue 2: 167 - 193

DOI: https://doi.org/10.1007/s11464-008-0021-1

Hamiltonian systems as selfdual equations

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  • Department of Mathematics, University of British Columbia;

Published date: 05 Jun 2008

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Abstract

Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action functionals obtained by a generalization of Bogomolnyi’s trick of ‘completing squares’. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the corresponding Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.

Cite this article

GHOUSSOUB Nassif . Hamiltonian systems as selfdual equations[J]. Frontiers of Mathematics in China, 2008 , 3(2) : 167 -193 . DOI: 10.1007/s11464-008-0021-1

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