Symplectic Geometry Applied to Boundary Problems on Hamiltonian Difference Systems

Zhenlai Han; Shurong Sun

Symplectic Geometry Applied to Boundary Problems on Hamiltonian Difference Systems

Authors

Zhenlai Han Institute of Applied Mathematics, Naval Aeronautical Engineering Institute, Yantai, 264001, P.R. China.
Shurong Sun School of mathematics, Shandong University, Jinan, 250100, P.R. China and School of Science, Jinan University, Jinan, 250022, P.R. China.

Keywords:

Hamiltonian difference system, boundary space, symplectic invariant, boundary condition

Abstract

In this work, we consider the boundary problem for Hamiltonian difference system

on an discrete interval I. Applying the concept of symplectic geometry, we give a complete account to the form of all possible symmetric boundary conditions with respect to separation or coupling at the endpoints for the complete Lagrangian space, following the development of the GKN-theory.