Sesión Geometría y Teoría de LiePoisson-Lie groups and invariant volume forms for Hamiltonians dynamics
Edith Padrón Fernández
Universidad de La Laguna, España - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
A Poisson-Lie group is a Lie group endowed with a Poisson structure such that the multiplication is a Poisson map. Hamiltonian systems on Poisson-Lie groups appear in the differential equation approach to the singular value decomposition (SVD) of a bidiagonal matrix. On the other hand, an approach to the integrability of a dynamical system on a manifold of dimensión n, following Euler and Jacobi, is to look for n−2 functionally independent first integrals and an invariant volume form. Under these conditions, the system can be integrated by quadratures (by means of a finite number of algebraic operations and quadratures of some functions). In this talk, we discuss the relation between the existence of invariant volume forms for Hamiltonian systems on Poisson-Lie groups and the unimodularity of the Poisson-Lie structure.
Referencias
[1] Journal of Physics A: Mathematical and Theoretical, Vol. 56, Núm. 1