Daremos condições explícitas (que definem um conjunto C1-aberto de difeomor- fismos) que garantem a existência de medidas ergódicas não-hiperbólicas com entropia positiva.
Para isso, estabelecemos um critério que garante a existência de um conjunto parcialmente hiperbólico com direção central unidimensional e entropia positiva cujo expoente central é zero de forma uniforme.
Three-dimensional symmetries are often observed as 2-dimensional objects. In
this seminar we will provide a description of which 3-dimensional lattices may produce
2-dimensional projected pattern with hexagonal symmetries. As an application we compare
some projected spatially periodic functions, also called planforms, with bifurcation
problems deﬁned in two-dimensions.
An impulsive semiflow is prescribed by three ingredients: a continuous semiflow on a compact metric space X which governs the state of the system between impulses; a set D ⊂ X where the flow undergoes some abrupt perturbations, whose duration is, however, negligible in comparison with the time length of the whole process; and an impulsive function I: D → X which specifies how a jump event happens each time a trajectory of the flow hits D, whose action may be a source of discontinuities on the trajectories.
We consider nonwandering dynamics near heteroclinic cycles between two hyper- bolic equilibria. The constituting heteroclinic connections are assumed to be such that one of them is transverse and isolated. Such heteroclinic cycles are associated with the termination of a branch of homoclinic solutions, and called T-points in this context. We study codimension-two T-points and their unfoldings in Rn. In our consideration we dis- tinguish between cases with real and complex leading eigenvalues of the equilibria.
In the theory of coupled cell networks, formalized by Ian Stewart, Martin Golu- bitsky and coworkers, a cell is a dynamical system and a coupled cell system is a finite collection of interacting cells. A coupled cell system can be associated with a network - a directed graph whose nodes represent cells and whose arrows represent couplings between cells. Given a network, it is potentially of wide interest to study when distinct individuals exhibit identical dynamics, being synchronized, for every admissible vector field, consis- tent with the structure of the network.
É um problema antigo em sistemas dinâmicos perceber como a estabilidade de uma certa propriedade no espaço de fase implica algum comportamento do tipo hiperbólico na aplicação tangente do sistema.
A estabilidade de certas propriedades como conjugação topológica, estabilidade sombre- amento, especificação entre outras têm sido um assunto em análise nos últimos anos. O nosso interesse é na propriedade de sombreamento fraco.
Given a continuous map T : X → X on a compact metric space X, we consider the push forward map T♯ : P(X) → P(X), and analyze how the dynamics of T relates to the dynamics of T♯ on the space of prob measures P(X).
In this talk we will discuss the conjugacy classes of Gevrey vector ﬁelds close to constant vectors with Brjuno type arithmetic condition. Our main tool is a renormalization method based on a multidimensional continued fraction expansion. This is a joint work with João Lopes Dias.