Seminario Geometría, Mecánica y Control
Jacobi Hamiltonian Integrators: from construction to examples
Ponente: Gonçalo Oliveira (Instituto Superior Technique Lisboa)Fecha: jueves 21 de mayo de 2026 - 12:00Lugar: Aula Gris 3, ICMAT
Online: Zoom. Meeting ID: 810 9248 3225; Access code: 183643
Resumen:
Jacobi manifolds provide a unified geometric framework generalising both Poisson and contact manifolds, and arise naturally in a wide range of physical systems - from damped oscillators to rigid body dynamics. This talk presents a systematic construction of structure-preserving numerical integrators for Hamiltonian systems on Jacobi manifolds, built upon the theory of homogeneous symplectic groupoids, poissonization, and a Hamilton-Jacobi generating function approach.The resulting Jacobi Hamiltonian Integrators (JHI) achieve high convergence orders while respecting the underlying geometric structure over long time horizons, a property that standard methods such as Runge-Kutta fail to guarantee. We illustrate the theory through several concrete examples, including the damped harmonic oscillator, Lotka-Volterra systems, and rigid body rotation, supported by numerical experiments demonstrating the superiority of the method.
