Description

The LxDS-Lisbon Dynamical Systems group, the Mathematics Departments of ISEG and FCUL, and the research centers CEMAPRE (ISEG Research) and CEMS.UL, are organizing a 3-day spring school (27th-29th May 2026) 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, 2026. 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.

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

ISEG Research - UID/06522/2025 and

Center For Mathematical Studies - CEMS.UL - UID/04561/2025

 Speakers:

Carlos Matheus

(Institut Polytechnique de Paris)


Maria Joana Torres

(University of Minho)

Fejoz Jacques

(Université Paris Dauphine-PSL)

Outline:

Theta-simplicity of the Lyapunov spectrum of locally constant cocycles over almost uniformly hyperbolic flows (Carlos Matheus)

The features of the Lyapunov exponents are often important in many applications of dynamical ideas. Partly motivated by this scenario, Avila and Viana famously established in 2007 the Kontsevich-Zorich conjecture on the simplicity of the Lyapunov exponents of the Kontsevich-Zorich cocycle with respect to the Masur-Veech measures. Nonetheless, it is known (by the works of Filip, Forni, Avila, Yoccoz and myself) that the Lyapunov spectrum of the Kontsevich-Zorich cocycle with respect to other interesting measures can be much richer in general. In this minicourse, after reviewing in detail the proof of Furstenberg's theorem about random walks on SL(2,R), we shall discuss a joint work with F. Arana-Herrera, J. De Witt, A. Eskin, V. Gadre, R. Gutierrez-Romo, Y. Lima, K. Rafi and S. Schleimer about the Theta-simplicity of locally constant cocycles over almost uniformly hyperbolic flows (such as the Kontsevich-Zorich cocycle over the support of SL(2,R)-invariant probability measures).

Isospectral reduction and network dynamics (Maria Joana Torres)

Leonid Bunimovich and Benjamin Webb introduced an important tool, the isospectral reduction, for analyzing network/graph dynamics. Isospectral reductions reduce the dimension of a matrix/graph while preserving its eigenvalues and eigenvectors. More recently, this theory was extended to infinite graphs. In this mini-course, we present an overview of isospectral reduction theory and its applications to network dynamics.

(1) How to reduce a network preserving its spectrum?

Isospectral reduction theory of Leonid Bunimovich and Benjamin Webb.

(2) Eigenvectors of isospectral transformations.

(3) Isospectral reduction and stationary measures on infinite graphs.

(4) What is the asymptotic behaviour of a real-world network?

Applications of isospectral reduction to the dynamics of real-world networks.

t.b.a. (Fejoz Jacques)

t.b.a.

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)

Pedro Soares

(Universidade de Lisboa)

Target Audience

PhD students, post-docs and researchers.

Accommodation

For more information please contact us.

Supporting institutions