Fredholm pseudo-gradients for the action functional on a sub-manifold of dual Legendrian curves of a three dimensional contact manifold (M3, α)
Tóm tắt
We prove in this paper that the intersection numbers between periodic orbits have an intrinsic meaning for the variational problem (J,C
β
) {Bahri (Pseudo-Orbits of Contact Forms Pitman Research Notes in Mathematics Series No. 173, 1984), Bahri (C R Acad Sci Paris 299, Serie I 15:757–760, 1984), Bahri (Classical and Quantic periodic motions of multiply polarized spin-manifolds. Pitman Research Notes in Mathematics Series No. 378, 1998)}, corresponding to the periodic orbit problem on a sub-manifold of the loop space of a three dimensional compact contact manifold (M, α).
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