Noticias en español
Predictive sets
ABSTRACT: A subset of the integers P is called predictive if for all zero-entropy processes X_i; i in Z, X_0 can be determined by X_i; i in P. The classical formula for entropy shows that the set of natural numbers forms a predictive set. In joint work with Benjamin Weiss, we will explore some necessary and some sufficient conditions for a set to be predictive. These sets are related to Riesz sets (as defined by Y. Meyer) which arise in the study of singular measures. This and several questions will be discussed during the talk. No previous background will be assumed on the subject.
Read MoreDynamics of unipotent frame flows on hyperbolic manifolds.
ABSTRACT: Joint work with B. Schapira. After explaining the geometry of the objects, we give another proof of a theorem of A. Mohammadi and H. Oh about the ergodicity of the Burger-Roblin measure for Kleinian groups of high enough critical exponents, and relate it with a topological counterpart.
Read MoreDynamics of unipotent frame flows on hyperbolic manifolds
ABSTRACT: Joint work with B. Schapira. After explaining the geometry of the objects, we give another proof of a theorem of A. Mohammadi and H. Oh about the ergodicity of the Burger-Roblin measure for Kleinian groups of high enough critical exponents and relate it with a topological counterpart.
Read MoreAplicaciones de la teoría de forzamiento para los homeomorfismos del anillo compacto
ABSTRACT En esta charla presentaremos una introducción a la teoría de forzamiento de trayectorias transversas para homeomorfismos de superficie. Usando esta teoría, estudiamos los conjuntos de rotación de los homeomorfismos del anillo compacto que son isotópicos a la identidad. Probamos que si un tal homeomorfismo preserva el área, entonces todo número en su conjunto de rotación es realizado por un conjunto compacto e invariante. Trabajo con Fábio Tal.
Read MoreLower bounds on the Hausdorff dimension of the Rauzy gasket
ABSTRACT: The Rauzy gasket is an important fractal object arising in several dynamical constructions, such as Novikov’s problem and some renormalization schemes for certain families of interval exchange maps. It was conjectured by Novikov and Maltsev in 2003 that the Hausdorff dimension D of the Rauzy gasket is strictly comprised between 1 and 2. In 2016, Avila, Hubert and Skripchenko confirmed the upper bound D<2. In this talk, I will explain how to use the thermodynamical results of Cao, Pesin and Zhao to show that D > 1.19. This is joint work with Carlos Matheus.
Read MoreProblemas clásicos en EDO desde un punto de vista no autónomo
ABSTRACT: En esta charla daremos a conocer las versiones no autónomas de los clásicos problemas de estabilidad global y linealización suave. Además haremos un link entre el problema de estabilidad global autónomo y la conjetura jacobiana.
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