Dia: Dimecres, 4 d'octubre de 2023
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Filippo Giuliani (Politecnico de Milano)
Títol: Sobolev instability for the cubic NLS on irrational tori.
Resum: In the last two decades the study of instability in Sobolev spaces for nonlinear Hamiltonian partial differential equations on compact manifolds has drawn lots of attention in the mathematical community. A breaktrough result in this sense is due to Colliander-Keel-Staffilani-Takaoka-Tao (Invent. Math 2010), who showed the existence of solutions to the defocusing cubic NLS on the 2-dimensional square torus with arbitrarily small initial data and arbitrarily large Sobolev norms at later times. The mechanism to construct such unstable solutions is based on the study of the resonant dynamics of NLS and it has inspired several other works. However, Staffilani noticed that the same strategy would not applied for the NLS equation on 2-dimensional irrational tori, where the resonant structure is less rich.In this talk we discuss how we overcame this problem to prove Sobolev instability for the cubic NLS on irrational tori. Moroever, we present a recent result of this type where we take into account also the presence of smooth convolution potentials.
Dia: Dimecres, 25 d'octubre de 2023
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Román Moreno (UPC)
Títol: Splitting of separatrices for rapid degenerate perturbations of the classical pendulum
Resum: In this talk we will discuss the splitting distance of a rapidly perturbed pendulum
Dia: Dimecres, 29 de novembre de 2023
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Mar Giralt (IMCCE de l'Observatoire de Paris)
Títol: An Arnold diffusion mechanism for the Galileo satellites
Resum: Among the various actions that are being taken to preserve the circumterrestrial environment, end-of-life disposal solutions play a key role. In this regard, innovative strategies should be conceived not only by means of novel technologies, but also following an advanced theoretical understanding.
A growing effort is devoted to exploit natural perturbations to lead the satellites towards an atmospheric reentry. In the case of the Medium Earth Orbit region, home of the navigation satellite Galileo, the main driver is the gravitational perturbation due to the Moon, that can increase the eccentricity in the long term. In this way, the pericenter altitude gets into the atmospheric drag domain and the satellite eventually reenters.
This is a joint work with Elisa Maria Alessi (IMATI), Inma Baldomá (UPC), Marcel Guardia (UB) and Alexandre Pousse (IMATI).
Last updated: Thursday, 07-Dec-2023 12:27:33 CET