Multiplicity of characteristics with Lagrangian boundary values on symmetric star-shaped hypersurfaces
In the space \(\mathbb R^{2n}\) with the standard symplectic form, two Lagrangian subspaces are given together with a compact \(C^2\) hypersurface, which is star-shaped and symmetric with respect to the origin. It is proved that there is infinitely many Lagrangian orbits placed on the hypersurface, beginning on one Lagrangian subspace and ending on the other. This is a generalization of the result when two Lagrangian subspaces coincide, which is proved in \textit{F. Luo} and \textit{C. Liu} [Nonlinear Anal., Theory Methods Appl. 69, 1425--1436 (2008; Zbl 1153.37407)].
scientific article; zbMATH DE number 5549407
scientific article