DSNT Seminar: A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems

Abstract: In KAM theory, constructive techniques are essential in order to produce realistic results in physical problems, since there is usually a big gap between purely analytical results and numerical ones. In this talk, I will present an algorithm for computing lower-dimensional elliptic tori in Hamiltonian systems based on a parametrization method. In this extension of KAM theorem, the focus is on tori that are characterized by a quasi-periodic motion with a lower number of frequencies than the degrees of freedom of the system. Moreover, the linear dynamics in the transverse dimensions is elliptic. Unlike other approaches based on normal forms methods, the parametrization method does not require the Hamiltonian to be nearly-integrable nor expressed in action-angle variables. Furthermore, our algorithm fixes both the frequency vectors involved in the dynamics, the one describing the quasi-periodic motion on the torus and the one related to the harmonic oscillations in the transverse dimensions. As an example, I will discuss an application of the algorithm to compute lower dimensional tori in a model that involves four coupled pendula. This is a joint work with J-L. Figueras and A. Haro.  

For more information, please contact the organiser Reza Mohammadpour.

This is a seminar in our seminar series on Dynamical Systems and Number Theory (DSNT).