Invited Speakers

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All are welcome to participate, there is no registration fee.  Please register in the link above. 

Participants 

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Poster

Program:

Alexandre Rodrigues (ISEG, University of Lisbon)

Title:  The Bosch and Simó Conjecture on the Shilnikov-Hopf Bifurcation

Abstract:  In this talk, I provide a rigorous mathematical proof of the Bosch-Simó conjecture (M. Bosch, C. Simó  (1993), Physica D, 217–229) regarding the abundance of strange attractors in the unfolding of a Shilnikov-Hopf bifurcation. By constructing a general class of dissipative return maps that capture the essential global geometry of this codimension two scenario, we demonstrate that "large” strange attractors – in the sense of Broer-Simó-Tatjer – are a persistent robust feature of the dynamics.

Ana Rodrigues (University of Évora)

Title:  Piecewise Isometries

Abstract: In this talk we will introduce Piecewise Isometries as Dynamical Systems. We will further discuss recente results on the dynamics of such systems (relation with Interval Exchange Transformations, existence of invariante curves, etc) and future directions of research. This is joint work with Arek Goetz, Peter Ashwin, Pedro Peres and Noah Cockram.  The speaker acknowledges the support of CIMA – Centro de Investigação em Matemática e Aplicações and the financial support of the FCT – Fundação para a Ciência e a Tecnologia under the project UID/4674/2025.

Hector Barge (Technical University of Madrid)

Title:  Continuations and bifurcations of attractors of discrete dynamical systems

Abstract:  In this talk we shall study continuations of attractors of embeddings in manifolds. We shall introduce the abstract basin of attraction of such attractors and we shall see that if two attractors are related by continuation, their abstract basins are homeomorphic. Moreover, if this continuation is achieved by a small perturbation, then, the homeomorphism can be chosen to be the identity close to the original attractor. We shall make use of this rigidity property in order to characterize the Cech cohomology of the attractors expelled after a generalized Hopf bifurcation of an attractor.  These results have been obtained in collaboration with J. Sánchez-Gabites

Jaime Sánchez-Gabites (Autonomous University of Madrid)

Title:  Universal bounds on the entropy of toroidal attractors

Abstract: A compact subset K of IR^3 is called toroidal if it has a neighbourhood basis of solid tori. To any toroidal set one can assign a finite set of prime numbers called its prime divisors. These reflect purely topological properties of K.   Suppose K is a toroidal set and f is a diffeomorphism of IR^3 which realizes K as an attractor (solenoids are the canonical example of this). We prove the following: the entropy of f|_K is bounded below by \log p_1 ... p_r, where the p_i are the prime divisors of K. Since the latter depend only on K, this provides a universal lower bound on any attracting dynamics on K.  In this talk we will discuss the main geometric tool used to prove this and consider the (plausible?) validity of the result when f is only a homeomorphism.

Jorge Freitas (University of Porto)

Title:  Multivariate extremes for dynamically generated processes

Abstract:  We study the cross-sectional dependence of multivariate observations along the systems’ orbits. We show that the componentwise dependence results from the combination of a spatial and a temporal dependence structures. We give several illustrative applications, where concrete systems and dependence sources are introduced and analysed

Marcelo Durães (Faculty of Sciences, University of Lisbon)

Title:  Random 2D Singular Cocycles: Dichotomic Behaviour of the Lyapunov Exponent

Abstract: The continuity of the Lyapunov exponents was proved by Bocker  and Viana in the setting of random invertible two dimensional cocycles. (This result has also been extended recently to d-dimensional  cocycles by Avila, Eskin and Viana.) It is well known that in the non-invertible scenario the continuity does not hold. In this talk, I will introduce a dichotomous result with the flavour  of Mañé-Bochi’s Theorem. For random non-invertible two dimensional cocycles, either the cocycle admits a dominated splitting, or  it can be approximated by cocycles with Lyapunov exponent equal to −∞. As a consequence, either the Lyapunov exponent is analytic or it is discontinuous. This is a joint work with Pedro Duarte, Tomé Graxinha and Silvius Klein.

Pedro Duarte (Faculty of Sciences, University of Lisbon)

Title:  Regularity of the Lyapunov exponents for finitely supported random linear cocycles with values in GL(d,R).  

Abstract: Weaker Hölder regularity of the first Lyapunov exponent for finitely supported random linear cocycles with values in GL(d,R) when the top Lyapunov exponent is simple. This is a work in progress with Marcelo Durães, Silvius Klein and Tomé Graxinha, on a preliminary quantitative version of a recent result of Avila, Eskin and Viana (https://arxiv.org/abs/2305.06009).

Ramón Barral (Technical University Madrid)

Title:  Mean equicontinuity, flows spaces and foliation theory

Abstract:  The concept of mean equicontinuity is undoubtedly one of the most important areas of  research in dynamical systems theory, lying at the intersection of topological and measure theory. In  this talk, we will study this concept for flow spaces—that is, one-dimensional compact metric spaces  admitting a fixed-point-free action of the real line—, where there is a strong correlation between  topology and the possible dynamics. In order to do that, we will use equicontinuous laminations  as topological substitutes for the role played by maximal equicontinuous factors in the category of  group actions.

Telmo Peixe (ISEG, University of Lisbon)

Title:  A projective-map approach to the stability of heteroclinic networks

Abstract: Heteroclinic networks frequently arise in evolutionary game dynamics and provide a rich source of complex asymptotic behaviour. In this talk, we present an asymptotic framework for analysing the stability of heteroclinic cycles in a one-parameter family of polymatrix replicator systems. The network under consideration is contained in a three-dimensional invariant manifold and consists of six interconnected heteroclinic cycles.  Our approach is based on reducing the essential dynamics near the network to a one-dimensional return map, referred to as the \emph{projective map}. This reduction provides an effective criterion for determining both the asymptotic stability of the network and the cycle that is observed in numerical simulations. In particular, the stability properties of the fixed points of the projective map are shown to characterise the stability of the corresponding heteroclinic cycles.  The proposed methodology is not restricted to the present model and can be extended to a broader class of heteroclinic networks, offering a useful tool for the study of computational and asymptotic dynamics.  This is joint work with Alexandre Rodrigues (ISEG, ISEG Research, Universidade de Lisboa).

Anfiteatro Sousa Pinto, Department of Mathematics, Universidade de Aveiro

How to arrive

From Lisbon:

There is a Metro leaving the airport and going to Estação do Oriente. There are regular trains from Lisbon to Aveiro, just pay attention to different duration of the trip and prices.

From Porto Airport:

There is a Flixbus direct bus from Porto Airport to the train station in Aveiro.  Alternatively, there is a Metro leaving the airport and going to the Campanhã Train Station. There are regular trains from Porto to Aveiro, just pay attention to different duration of the trip and prices.

In Aveiro:

The Mathematics Department of the University of Aveiro is located at 2.4 km from the Train Station, and it takes about 30 minutes walking. There is also the option of taking a Taxi or an Uber. 

Supported by CIDMA under the Portuguese Foundation for Science and Technology (FCT, https://ror.org/00snfqn58)  Multi-Annual Financing Program for \&D Units, grants UID/4106/2025 and UID/PRR/4106/2025