Dia: Dimecres 14 de gener de 2026
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Renato Calleja (UNAM)
Títol: Invariant Tori in Hamiltonian and conformal-Hamiltonian Systems: Constructive and Geometric Perspectives
Resum: This talk presents recent and ongoing work on invariant tori in Hamiltonian systems with quasi-periodic time dependence, combining geometric insight and computational techniques. In collaboration with Pedro Porras and Alex Haro, we developed an a-posteriori KAM theorem for Lagrangian tori in flows, solved via a Newton-like scheme using symplectic frames and a new torsion matrix formulation. The method yields efficient, quadratically convergent algorithms under classical Diophantine and non-degeneracy conditions.
We also discuss results for conformally symplectic (dissipative) systems, including the spin–orbit problem and the breakdown of quasi-periodic attractors. Current joint work with Alex Haro and Arturo Vieiro explores secondary tori near elliptic points and resonance capture via Birkhoff normal forms.
The parameterization method serves as a unifying framework throughout, bridging conservative and dissipative regimes and linking rigorous theory with effective computation.
Last updated: Tue Jan 27 15:46:24 2026