Our talk is concerned with the study of dynamical systems which are piecewise contraction maps (PC maps). Certain mathematical models, like contracting outer billi- ards and switched flow systems, are described by PC maps. In the setup, one considers a convex subset X ⊂ Rd and a finite partition of X: X1,...,Xn. Then the map f : X → X is assumed to be a contraction on each element Xi of the partition. It is expected that a typical PC map has finitely many periodic orbits and every orbit converges to a periodic orbit.
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity.
Consideramos um processo estocástico estacionário discreto e sobre um alfabeto finito ou enumerável. Definimos o período de uma sequência de tamanho n. Apresentamos teoremas assindéticos para esta quantidade: seu crescimento linear concentrado, seus grandes desvios relacionados à entropia de Renyi, suas flutuações e máximo (re-normalizados) e suas propriedades que descrevem a complexidade do processo. Ilustramos com alguns exemplos.
It is often relatively easy to identify and classify large classes of robust heteroclinic networks and cycles in certain classes of equivariant dynamics and systems governed by generalized Lotka-Volterra equations. On the other hand, there is a lack of methods for identifying and classifying heteroclinic networks in coupled identical cell systems. We describe results that enable one to transform known results about systems governed by
I. Labouriau, Amadeu Delshams, D. Turaev, P. Ashwin, A. Lohse
Friday, 12 February, 2016 - 09:30
Heteroclinic Phenomena: the role of symmetry is a one-day meeting bringing together both experts and young researchers in the field. A small set of talks will set the pace for a discussion on the role of symmetry (reversing and preserving) in the occurrence and study of heteroclinic phenomena.
There is no registration fee. If you want to participate, please email both organisers.
O estudo de centralizadores, iniciado nos anos 60 e que corresponde essencialmente ao estudo de simetrias no sistema dinâmico, tem tido
diversas contribuições. As simetrias são entendidas no sentido de que, se um difeomorfismo pertence ao centralizador de um dado difeomorfismo
ele comuta com o mesmo e portanto a sua ação preserva as órbitas do sistema dinâmico. Uma descrição da 'quantidade' de sistemas dinâmicos que possuem simetrias é um problema importante com ligações à física. Smale conjecturou que tipicamente (aberto e denso, Baire genérico, ...) no
Silvius Klein (Norwegian University of Science and Technology, Norway)
Friday, 27 November, 2015 - 14:30
In some previous works, P. Duarte and I have developed an abstract scheme of
proving continuity properties of the Lyapunov exponents and of the Oseledets filtration
associated with general linear cocycles, by means of large deviation type estimates. The
purpose of this talk is to describe a recent result that fits this abstract scheme, concerning
analytic quasi-periodic cocycles on the higher dimensional torus. The main new feature
of this result is allowing the determinant of the matrix-valued function defining the linear
Wescley Bonomo (Universidade Federal da Bahia, Brasil)
Friday, 13 November, 2015 - 14:30
In seminal papers Smale conjectured that most diffeomorphisms should have trivial centralizer. That is, maps commuting with the original dynamical system are necessarily a power of it. Also, a similar conjecture about centralizers of smooth flows can be formulated. In this context, we present a result obtained with Paulo Varandas (UFBA) and Jorge Rocha (UP) about the existence of an open and dense subset of Komuro-expansive fields with singularities whose elements have centralizer unstable.
In this talk we introduce a model for the dynamics of HIV epidemics under distinct HAART regimes, and study the emergence of drug-resistance. The model predicts HIV dynamics of untreated HIV patients for all stages of the infection. We compute the local and the global stability of the disease-free equilibrium of the model. We simulate the model for two distinct HIV patients, the rapid progressors and the long-term non- progressors. We study the effects of equal RTI and PI efficacies, as well as distinct drug efficacies, namely RTI-based and PI-based therapeutics.
Tomás Lázaro (Universitat Politècnica de Catalunya, Spain)
Friday, 20 November, 2015 - 15:30
One of the main interest studying reversible systems is the fact that they can exhibit, simultaneously, both conservative and dissipative-like behaviour. In our context, we will consider diffeomorphisms which are smoothly conjugate to their inverse map through an involution $R$ ($R^2=Id$, $R\neq 0$). They are referred as $R$-reversible or, simply, reversible maps.