On Symplectic and Multisymplectic Srtuctures and Their Discrete Versions in Lagrangian Formalism
نویسنده
چکیده
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 their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variasional principle with the difference being regarded as an entire geometric object and the noncommutative differential calculus on regular lattice. In order to show that in all these cases the symplectic and multisymplectic preserving properties do not dependant on the relevant Euler-Lagrange equations, the Euler-Lagrange cohomological concepts and content in the configuration space are employed.
منابع مشابه
Difference Discrete Variational Principle , Euler - Lagrange Cohomology and Symplectic , Multisymplectic Structures
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 view of noncomutative differential geometry. By virtue of this variational principle, we get the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical ...
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