LxDS Spring School 2024

Workshop

27-29 May 2024, FCUL-Faculdade de Ciências, Universidade de Lisboa

Description

The LxDS-Lisbon Dynamical Systems group, the Mathematics Department of ISEG and FCUL, CEMAPRE, REM and CMAFcIO are organizing a 3-day spring school (27th to 29th May 2024) on dynamical systems to be held at FCUL/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 by April 30, 2024. Please fill the form on this web page.

Those wishing to give a 20-minute talk should mention it in the comments section of the registration form, indicating the corresponding title and abstract.

The spring school will have a limited number of participants.

PhD students can apply for financial support (deadline - April 21, 2024).

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

This event is supported by national funds through FCT – Foundation for Science and Technology, projects

CEMAPRE/REM - UIDB /05069/2020 - https://doi.org/10.54499/UIDB/05069/2020 and

CMAFcIO - UIDB/04561/2020 - https://doi.org/10.54499/UIDB/04561/2020

Speakers:

Tere M-Seara

(Universitat Politècnica de Catalunya) 

Peter Ashwin

(University of Exeter)

Paulo Varandas

(Universidade Federal da Bahia)

Organizers:

Pedro Duarte

(Universidade de Lisboa) 

João Lopes Dias

(Universidade de Lisboa)

José Pedro Gaivão

(Universidade de Lisboa) 

Telmo Peixe

(Universidade de Lisboa)

Alexandre Rodrigues

(Universidade de Lisboa)

Outline:

Arnold diffusion through geometric methods (Tere M-Seara)

In this course, we will revise the so-called geometric methods which have prove being very useful to detect the existence of Arnold diffusion in a given system, as well as to produce results for typical ones. We will recall the basic tools: normally hyperbolic invariant manifolds, scattering maps, heteroclinic chains of tori of different topology and we will show how the combination of these tools makes apparent several mechanisms of diffusion. We will also show some new ideas which do not need the use of heteroclinc chains to provide diffusion. Some applications to celestial mechanics will be given.

Nonautonomous dynamical systems: theory and applications (Peter Ashwin)

I will introduce some concepts used to understand the behaviour of nonautonomous dynamical systems such as ordinary differential equations with time dependent forcing. These have a parameter that changes with time in a deterministic but not necessarily recurrent or stationary manner. Focussing especially on systems that are asymptotically autonomous, the asymptotic dynamics can be connected in nontrivial ways to the nonautonomous dynamics and nonautonomous instabilities (tipping points) may appear through various mechanisms, including breakdown of an adiabatic approximation. I will discuss this along with some motivating examples.

Topological and ergodic properties of hyperbolic flows (Paulo Varandas)

Uniformly hyperbolic diffeomorphisms have been intensively studied by many authors since the sixties, and much is known about their topological, geometric and ergodic properties. For instance, it is well known that under a transitivity assumption such diffeomorphisms have unique equilibrium states for Holder continuous potentials, these satisfy a Gibbs property and have exponential decay of correlations for Holder continuous observables. Even though the general picture for uniformly hyperbolic flows is expected to be somewhat similar, there are still some major open questions which really highlight the difference between these discrete and continuous time dynamical systems. In this minicourse I will address on the thermodynamic formalism of hyperbolic flows with particular emphasis on their decay of correlations.

Target Audience

PhD students, post-docs and researchers.

Venue

FCUL, Building C6, Room t.b.a.

Accommodation

For more information please contact us.

Supporting institutions