Dynamical Systems

Multidimensional continued fractions and symbolic dynamics for toral translations

Event Date: May 31, 2018 in Dynamical Systems, Seminars

ABSTRACT:  We give a dynamical, symbolic and geometric interpretation to multi-dimensional continued fractions algorithms. For some strongly convergent algorithms, the construction gives symbolic dynamics of sublinear complexity for almost all toral translations; it can be used to obtain a symbolic model of the diagonal flow on lattices in $\mathbb R^3$.

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Entropías intermedias y temperatura nula en curvatura negativa

Event Date: May 28, 2018 in Dynamical Systems, Seminars

ABSTRACT:     Un problema bastante general en teoría ergódica consiste en estudiar al conjunto de entropías de un sistema dinámico respecto a sus medidas ergódicas. Katok conjeturó que dicho conjunto contiene al intervalo $[0,h_{top}(f))$ en el caso de difeomorfismos suaves en variedades compactas. Si bien la conjetura permanece abierta, muchos avances se han logrado a la fecha. Se conoce, por ejemplo, que el flujo geodésico en variedades compactas a curvatura negativa verifica esta propiedad. La demostración de esto último recae en la realización del flujo geodésico como un flujo de...

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Invariant Random Subgroups of Full Groups of Bratteli diagrams

Event Date: May 22, 2018 in Dynamical Systems, Seminars

ABSTRACT:   In the talk, we will classify the ergodic invariant random subgroups (IRS) of simple AF full groups. AF full groups arise as the transformation groups of Bratteli diagrams that preserve the cofinality of infinite paths in the diagram.  AF full groups are complete (algebraic) invariants for the isomorphism of Bratteli diagrams. Given a simple AF full group G, we will prove that every ergodic IRS of G arises as the stabilizer distribution of a diagonal action on X^n for some n, where X is the path-space of the Bratteli diagram associated to G. This is joint work with Artem...

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Local rules for planar tilings

Event Date: Mar 12, 2018 in Dynamical Systems, Seminars

  ABSTRACT:  The cut and project method is one of the prominent method to define quasiperiodic tilings. In order to model quasicrystals, where energetic interactions are only short range, it is important to know which of these tilings can be characterized by local configurations (in dynamical terms: which of these tiling spaces are of finite type or sofic). In this talk we shall review known results, in particular those obtained these last years with Nicolas Bedaride and Mathieu Sablik.

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CURTIS-HEDLUND-LYNDON THEOREM FOR ULTRAGRAPH SHIFT SPACES

Event Date: Jan 22, 2018 in Dynamical Systems, Seminars

ABSTRACT: In this work we characterize the class of continuous shift commuting maps between ultragraph shift spaces, proving a Curtis-Hedlund-Lyndon type theorem. Then we use it to characterize continuous, shift commuting, length preserving maps in terms of generalized sliding block codes. This is a joint work with Prof. Daniel Gon\c{c}alves (UFSC, Brazil)

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Equidistribution of dilated curves.

Event Date: Jul 10, 2017 in Dynamical Systems, Seminars

Resumen:    Consider a light source located in a polynomial room. It is a classic question whether the whole room is illuminated by the light. This question was recently settled by Lelievre, Monteil and Weiss. In this talk, we study the variation on the illumination problem introduced by Chaika and Hubert in the context of closed curves on nilmanifolds. We give necessary and sufficient conditions for a nilmanifold being illuminated by a curve.

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