• Tingueu el micròfon apagat tota l'estona excepte durant el "Cafè i galetes".
• Podeu tenir la càmera encesa si voleu, però en cas de saturaciò de línies, caldrà que la tanqueu.
• Si voleu fer una pregunta, si us plau demaneu torn a través del xat i espereu que els moderadors us donin la paraula.
• Si és possible, entreu amb antelació. Els que no useu un compte de correu de la UPC haureu d'esperar a ser admesos per accedir-hi.

Dia: Dimecres, 4 d'octubre de 2023

Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.

• Hora: 16h00m

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.

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Dia: Dimecres, 25 d'octubre de 2023

Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.

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• Hora: 16h00m

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

H(x,y,t) = y²/2 + (cos(x)-1) + μ (cos(x)-1) g(t/ε)
with g(τ) a 2π-periodic function for which the first harmonic, g^[±1], is zero and μ,ε ≪ 1. Systems of this kind undergo exponentially small splitting of separatrices and, when μ ≪ 1, it is known that the Melnikov function actually gives an asymptotic expression for the splitting function provided g^[±1] is not 0. We will focus on the case g^[±1]=0, the main question being what the main term in the asymptotic expression of the splitting distance is in this case. We will present two results that answer this question and we will show an example of application to a couple of concrete systems. We will also present a sketch of the proof, which consists in using a splitting formula based on the solution of the so-called inner equation and making use of the Hamilton-Jacobi formalism.

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Dia: Dimecres, 29 de novembre de 2023

Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.

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• Hora: 16h00m

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).

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Sessió actual.

Last updated: Thursday, 07-Dec-2023 12:27:33 CET