LxDS Spring School 2019


29-31 May 2019, Faculdade de Ciências, Universidade de Lisboa, Lisboa


The LxDS-Lisbon Dynamical Systems group, the Mathematics Department of Ciências, ISEG, CEMAPRE, REM and CMAF-CIO are organizing a 3-day spring school (29th to 31st May) on dynamical systems to be held at Faculdade de Ciências/ULisboa. The school will consist of three mini-courses in specific areas of dynamical systems lectured by specialists of recognized international merit.

REGISTRATION is required to confirm participation. Please fill the form on this web page.
If you want to make a 15-minute oral presentation, mention this by indicating a title and summary in the "comments" section of the registration form.
The spring school will have a limited number of participants.
PhD students can apply for financial support.


Marcel Guardia (Universitat Politècnica de Catalunya),
Anders Karlsson (Université de Genève),
Jorge Freitas (Universidade do Porto).


Pedro Duarte (Universidade de Lisboa), José Pedro Gaivão (Universidade de Lisboa), João Lopes Dias (Universidade de Lisboa), Telmo Peixe (Universidade de Lisboa), Luís Sampaio (Universidade de Lisboa) and Filipe Santos (Instituto Superior de Economia e Gestão)


Transfer of energy in Hamiltonian PDEs (Marcel Guardia)

A fundamental question in Hamiltonian PDEs is the analysis of solutions which undergo transfer of energy from low to high modes as time evolves. Such transfer is usually measured by the growth of the Sobolev norms of the solutions. In these lectures we will review recent results constructing instability mechanisms which lead to such orbits for the nonlinear Schrödinger equation. These instability mechanisms rely on drifting along resonances as happens in the Arnold diffusion phenomenon in nearly integrable Hamiltonian systems. We will show how to use dynamical systems techniques to achieve such drift.

Multiplicative and subadditive ergodic theorems (Anders Karlsson)

In this mini-course I will explain new multiplicative and sub additive ergodic theorems, from a joint work with S. Gouëzel. 
1. Metric functionals and a metric spectral principle. Applications to various dynamical settings.
2. Subadditive ergodic theory.
3. Multiplicative ergodic theorems.

Extreme events for dynamical systems (Jorge Freitas)

We make a brief introduction to the theory of Extreme Values for dynamical systems and show the connection with the study of hitting times to shrinking targets on the phase space, which is tied with the recurrence properties of the system. The occurrence of rare events, which are detected by abnormally high observations for certain potentials (which are called exceedances), can be modelled by probabilistic tools such as point processes, which keep information about both the time occurrences of the exceedances as well as of their impact. We will be particularly interested in the week limit of such point processes both in the presence and absence of clustering of exceedances. The appearance of clustering of exceedances turns out to be related with the local periodicity of the system. The intensity of the clustering is measured by a parameter called the Extremal Index, which can ultimately be linked to the fractal properties of the set appearing as the limit of the shrinking targets.


TimeDay 1
29th May
Day 2
30th May
Day 3
31st May
10h00 - 11h30Marcel Guardia
(Hamiltonian PDEs)
Marcel Guardia
(Hamiltonian PDEs)
Marcel Guardia
(Hamiltonian PDEs)
11h30 - 11h45Coffee breakCoffee breakCoffee break
11h45 - 13h15Anders Karlsson
(Multipl. and Subad. Ergodic Thrms)
Anders Karlsson
(Multipl. and Subad. Ergodic Thrms)
Anders Karlsson
(Multipl. and Subad. Ergodic Thrms)
13h15 - 15h00LunchLunchLunch
15h00 - 16h30Jorge Freitas
(Extreme Events)
Jorge Freitas
(Extreme Events)
Jorge Freitas
(Extreme Events)
16h30 - 17h00Coffee break
Coffee break

17h00 - 17h30
Gladston Duarte
(Invariant Manifolds near L1 and L2 in the
Planar Restricted Three-Body Problem
Maria Correia
(Elliptic islands and ergodic component in a
billiard table with circular arc boundaries
17h30 - 18h00
Paulo Varandas
(On the space of solutions of the cohomological
equation for linear cocycles
Hélder Vilarinho
(Invariant manifolds for Random Dynamical Systems on
Banach Spaces exhibiting generalized dichotomies

20h00School dinner

Target audience

PhD students, post-docs and researchers.


For more information on how to get to Faculdade de Ciências please visit this link


For more information please visit this link


The organizers are grateful for the sponsorship of the CIM - Centro Internacional de Matemática


CEMAPRE - Centre for Applied Mathematics and Economics

Rua do Quelhas, n.º 6
1200-781 Lisboa

Email: cemapre@iseg.ulisboa.pt
Tel: (+351) 213 925 876