Dynamical Systems

Sobre a existência robusta de medidas ergódicas não-hiperbólicas

Speaker: 

Lorenzo Dias (PUC-Rio, Rio de Janeiro, Brasil)

Date: 

Friday, 23 January, 2015 - 14:30

Venue: 

Room M031

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.

Continuity of Lyapunov Exponents

Speaker: 

Pedro Duarte (CEMAPRE – ISEG, Universidade Técnica de Lisboa)

Date: 

Friday, 16 January, 2015 - 14:30

Venue: 

Room M031

Large deviation type estimates of a linear cocycle can be used to prove the continuity of its Lyapunov exponents.

This sentence synthesizes a recent work with Silvius Klein, that will be surveyed in this seminar. 

Hexagonal Projected Symmetries

Speaker: 

Juliane Oliveira (FCUP, CMUP)

Date: 

Friday, 12 December, 2014 - 14:30

Venue: 

Room M031

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.

Invariant probability measures for impulsive semiflows

Speaker: 

Maria Carvalho (FCUP, CMUP)

Date: 

Friday, 4 July, 2014 - 13:30

Venue: 

Room M031

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.

Studying the dynamics near a Bykov heteroclinic cycle using Lin’s method

Speaker: 

Kevin Webster (Imperial College of London, UK)

Date: 

Friday, 28 November, 2014 - 14:30

Venue: 

Room M031

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.

Special Jordan subspaces in coupled cell networks

Speaker: 

Célia Sofia Moreira (FCUP-CMUP)

Date: 

Friday, 27 June, 2014 - 13:30

Venue: 

Room M031

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.

Estabilidade do sombreamento fraco em sistemas que preservam o volume

Speaker: 

Sandra Vaz (Universidade da Beira Interior)

Date: 

Friday, 14 November, 2014 - 14:30

Venue: 

Room M031

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.

Linearization of Gevrey flows on the multidimensional torus

Speaker: 

José Pedro Gaivão

Date: 

Friday, 31 October, 2014 - 14:30

Venue: 

Room M031

 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.

 

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