The project supported by National Natural Science Foundation of China under Grant No.10626016;China Postdoctor Science Foundation of Henan University under Grant No.05YBZR014
We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizont...
We present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M,ω) via the highest Euler-Lagrange cohomology.It is shown that for every volume-preserving flow there are som...
In the previous papers I and II, we have studied the difference discrete variational principle and the Euler?Lagrange cohomology in the framework of multi-parameter differential approach. We have gotten the difference...
In this second paper of a series of papers, we explore the difference discrete versions for the Euler?Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in...
In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in vi...
We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler-Lagrange cohomological ...
We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore the...