Dynamical Systems

Generic iterated function systems on the circle

Speaker: 

A. Okunev

Date: 

Friday, 17 June, 2016 - 14:30

Venue: 

Room M031

An iterated function system (IFS) on a manifold M is a tuple of smooth maps f1, ...,fs : M → M. One of the reasons for studying IFS's is that they (more precisely, associated step skew products over Bernoulli shift) provide a nice model example of partially hyperbolic skew products. If some interesting robust property is found for the IFS's, it is often possible to find this property for a locally generic set of diffeomorphisms (see, e.g., [1]).

Contributions to the thermodynamic formalism of semigroup actions

Speaker: 

Paulo Varandas

Date: 

Friday, 13 May, 2016 - 13:30

Venue: 

Room 005

We will report on some recent results concerning the topological entropy and dynamics of continuous free semigroup actions. We give sufficient topological conditions for the topological entropy to be positive and to be given by the exponential growth rate of “non-autonomous” periodic points. In the case of semigroups of Ruelle-expanding maps,

Dynamics near T-points - Talk 2

Speaker: 

Jurgen Knobloch

Date: 

Friday, 6 May, 2016 - 13:30

In these talks we consider dynamics near heteroclinic cycles between two hyperbolic equilibria with different saddle indices.
For that purpose, in the first talk we establish Lin's method as a unified approach to study nonwandering dynamics near those networks.

Dynamics near T-points - Talk 1

Speaker: 

Jurgen Knobloch

Date: 

Thursday, 5 May, 2016 - 13:30

In these talks we consider dynamics near heteroclinic cycles between two hyperbolic equilibria with different saddle indices.
For that purpose, in the first talk we establish Lin's method as a unified approach to study nonwandering dynamics near those networks.

Invariant manifolds for flows on polytopes

Speaker: 

Pedro Duarte

Date: 

Friday, 29 April, 2016 - 13:30

We study flows on polytopes whose dynamics leave all faces of the polytope invariant.  We assume that every edge consists only of equilibria, or else contains no interior equilibrium. Then the edges (and vertexes) of the polytope form a heteroclinic network, referred as the  edge heteroclinic network. Such models, like the Replicator equation, arise naturally in Evolutinary Game Theory.

Point processes of rare events for dynamical systems

Speaker: 

Ana Cristina Freitas

Date: 

Friday, 22 April, 2016 - 13:30

We consider discrete time dynamical systems and show the linking between Extreme Value Laws and Hitting Time Statistics. The stochastic processes arise from dynamical systems by evaluating an observable function (which achieves a global maximum at a single point of the phase space) along the orbits of the system. We exploit the connection between these two approaches both in the absence and presence of clustering. Clustering means that the occurrence of rare events has a tendency to appear concentrated in time.

Dimensionality of Pattern Formation in Symmetric Physical Systems

Speaker: 

Juliane Oliveira

Date: 

Friday, 15 April, 2016 - 13:30

In the study of pattern formation in symmetric physical systems a 3-dimensional structure in thin domains is often modelled as 2-dimensional one. As a contrast, in this work we use the full 3-dimensionality of the problem to give a theoretical interpretation and possibly decide whether the pattern seen in such systems naturally occur in either 2- or 3- dimension. For this purpose, we are concerned with functions in 3-dimention that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. In particular, we introduc

Dinâmica dos bilhares duais poligonais com contração

Speaker: 

José Pedro Gaivão

Date: 

Friday, 8 April, 2016 - 13:30

Considere-se um polígono convexo. Dado um ponto x no complementar  do polígono existe uma única recta de suporte do polígono que passa  por x tal que o polígono se encontra à direita da recta.  Genericamente, a recta de suporte intersecta o polígono num dos  seus vértices v. Obtém-se assim um novo ponto y reflectindo x em  torno de v e contraindo sua distância relativamente ao vértice,  isto é, y=v+a(v-x) onde 0<a<1. A transformação definida é designada  por bilhar dual poligonal com contracção.

On equilibrium states for impulsive semiflows

Speaker: 

Jaqueline Siqueira

Date: 

Friday, 1 April, 2016 - 10:30

Impulsive dynamical systems may be interpreted as suitable mathematical models of real world phenomena that display abrupt changes in their behavior, and are described by three objects: a continuous semiflow on a metric space X; a set D contained in X; where the flow experiments sudden perturbations; and an impulsive function I : D → X; which determines the change on a trajectory each time it collides with the impulsive set D.

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