Multiplicity of characteristics with Lagrangian boundary values on symmetric star-shaped hypersurfaces

In this paper, the multiplicity of Lagrangian orbits on C 2 smooth compact symmetric star-shaped hypersurfaces with respect to the origin in R 2 n is studied. These Lagrangian orbits begin from one Lagrangian subspace and end on another. An infinitely many existence result is proved via Z 2 -index theory. This is a multiplicity result about the Arnold Chord Conjecture in some sense, and is a generalization of the problem about the multiplicity of Lagrangian orbits beginning from and ending on the same Lagrangian subspace which was considered in the authorsʹ previous paper [F. Guo, C. Liu, Multiplicity of Lagrangian orbits on symmetric star-shaped hypersurfaces, Nonlinear Anal. 69 (4) (2008) 1425–1436].