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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Two-time distribution for KPZ growth in one dimension

Event Date: May 29, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

Abstract:   Consider the height fluctuations H(x,t) at spatial point x and time t of one-dimensional growth models in the Kardar-Parisi-Zhang (KPZ) class. The spatial point process at a single time is known to converge at large time to the Airy processes (depending on the initial data). The multi-time process however is less well understood. In this talk, I will discuss the result by Johansson on the two-time problem, namely the joint distribution of (H(x,t),H(x,at)) with a>0, in the case of droplet initial data. I also show how to adapt his approach to the flat initial case. This is...

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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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A priori estimates for elliptic equations in $\mathbb R^N$ – a critical case

Event Date: Dec 11, 2017 in CAPDE, Seminars

Abstract:   Using the Moser’s iteraction method we obtain an a priori estimate for elliptic equations in whole euclidian space in a critical growth situation

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Dynamics of strongly interacting unstable two-solitons for generalized Korteweg-de Vries equations.

Event Date: Mar 12, 2018 in CAPDE, Seminars

Abstract.   Many evolution PDEs admit special solutions, called solitons, whose shape does not change in time. A multi-soliton is a solution which is close to a superposition of a finite number K of solitons placed at a large distance from each other. I am interested in describing multi-soliton dynamics for generalized Korteweg-de Vries equations. I will present a general method of formally predicting the time evolution of the centers and velocities of each soliton. Then I will discuss in detail the case K = 2, in particular in the regime of strong interactions, which occurs when the...

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