On the existence of Hamiltonian paths connecting Lagrangian submanifolds

Details On the existence of Hamiltonian paths connecting Lagrangian submanifolds On the existence of Hamiltonian paths connecting Lagrangian submanifolds

2005-08-18

arxiv.org/abs/math/0508356v1

Mathematics

Analysis of PDEs

12 pages. Updated versions --if any-- of this author's papers can be downloaded at http://www.pims.math.ca/~nassif/

Scientific paper

We use a new variational method --based on the theory of anti-selfdual Lagrangians developed in [2] and [3]-- to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in $\R^{2N}$. We also consider the case where the Hamiltonian is only semi-convex. A variational principle is also used to establish existence for the corresponding Cauchy problem. The case of periodic solutions will be considered in a forthcoming paper [5].

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