SEM. GEOMETRÍA Y TOPOLOGÍA: Cristina Sardon. "A geometric HamiltonJacobi theory for a NambuPoisson structure"
 Tuesday, 17 October
 Plaza de las Ciencias nº 3 Facultad de CC Matemáticas
Seminario de Geometría y Topología
Cristina Sardón
ICMAT
A geometric HamiltonJacobi theory
for a NambuPoisson structure
13:00. Sala 225
The HamiltonJacobi theory is a formulation of Classical Mechanics equivalent to other formulations as Newton's equations, Lagrangian or Hamiltonian Mechanics. It is particulary useful for the identification of conserved quantities of a mechanical system. The primordial observation of a geometric HamiltonJacobi equation is that if a Hamiltonian vector field XH can be projected into the configuration manifold by means of a 1form dW, then the integral curves of the projected vector field XdWHcan be transformed into integral curves of XH provided that W is a solution of the HamiltonJacobi equation. This interpretation has been applied to multiple settings: in nonhonolomic, singular Lagrangian Mechanics and classical field theories. Our aim is to apply the geometric HamiltonJacobi theory to systems endowed with a NambuPoisson structure. The NambuPoisson structure has shown its interest in the study physical systems described by several Hamiltonian functions. In this way, we will apply our theory to two interesting examples in the Physics literature: the thirdorder KummerSchwarz equations and a system of n copies of a firstorder differential Riccati equation. From these examples, we retrieve the original Nambu bracket in three dimensions and a generalization of the Nambu bracket to n dimensions, respectively.
