Data: 30/10/2018

Ora: 09:00:00

Descrizione:

After giving some basic examples of Lie groupoids, we will explain the rule of convolution of distributions on a Lie groupoid G and its relationship with the symplectic groupoid structure on T^*G found by Coste-Dazord-Weinstein. Secondly, we will explain how to develop a calculus for Fourier Integral Operators on a groupoid G. Finally, we will show that the one parameter group e^{itP}, t ∈ **R**, where P is a first order elliptic positive G-pseudodifferential operator, consists of G-FIOs in a weaker sense.

Data: 26/10/2018

Ora: 11:30:00

Descrizione:

In the restricted three-body problem, consecutive collision orbits arethose orbits which start and end at collisions with one of theprimaries. Interests for such orbits arise not only from mathematics butalso from various engineering problems. In this talk we shall discussthe existence of such orbits via the use of Rabinowitz-Floer theory.This is a joint work with Urs Frauenfelder.

]]>Data: 12/10/2018

Ora: 09:30:00

Descrizione:

A mathematical billiard is a system describing the inertial motion of a point mass inside a domain, with elastic reflections at the boundary. This simple model has been first proposed by G.D. Birkhoff as a mathematical playground where "it the formal side, usually so formidable in dynamics, almost completely disappears and only the interesting qualitative questions need to be considered".Since then billiards have captured much attention in many different contexts, becoming a very popular subject of investigation. Despite their apparently simple (local) dynamics, their qualitative dynamical properties are extremely non-local. This global influence on the dynamics translates into several intriguing rigidity phenomena, which are at the basis of several unanswered questions and conjectures.In this talk I shall focus on some of these questions. In particular, I shall describe some recent results related to the classification of integrable billiards (also known as Birkhoff conjecture).ÂÂÂ This talk is based on works in collaboration with V. Kaloshin and with G. Huang-V. Kaloshin.

]]>Data: 11/10/2018

Ora: 14:30:00

Descrizione:

We prove the existence of solutions to the classical Liouville equation which blows-upalong a smooth, simple and closed curve inside a doubly connected domain.The result has been obtained in collaboration with Giusi Vaira and Mike Kowalczyk.

]]>Data: 25/06/2018

Ora: 15:00:00

Descrizione:

A simple general theorem permits to look for time-dependent Lyapunov functions for Lagrangian systems. We show three cases where the research is successful: the mechanical systems with viscous fluid resistance and the conservative and dissipative Maxwell-Bloch equations of laser dynamics. By means of these Lyapunov functions we study some dynamical features.

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