On the Lie algebra structures connected with Hamiltonian dynamical systems

  • R. G. Smirnov

Abstract

We construct the hierarchies of master symmetries constituting Virasoro-type algebras for the Hamiltonian vector fields preserving a recursion operator. Similarly, repeatedly contracting a Hamiltonian vector field with the corresponding recursion operator, we define an Abelian Lie algebra of the thus obtained hierarchy of vector fields. The approach is shown to be applicable for the Volterra and Toda lattices.
Published
25.05.1997
How to Cite
SmirnovR. G. “On the Lie Algebra Structures Connected With Hamiltonian Dynamical Systems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 49, no. 5, May 1997, pp. 699–705, https://umj.imath.kiev.ua/index.php/umj/article/view/5051.
Section
Research articles