Noticias en español
Piecewise contraction maps and its applications
Abstract: Our talk concerns dynamical systems which are defined by piecewise contraction maps (PC maps). There is a large literature which deals with the dynamical behavior of PC maps defined on convex subsets of Euclidean spaces in different contexts. Our aim is to show that, under certain conditions, a typical PC map, in the measure theoretical sense of the parameter space, is asymptotically periodic which means that the map has finitely many periodic orbits and every orbit converges to a periodic orbit. Our setup is the following: We fix an Iterated Function System {φ1, . . . ,...
Read MoreLimit theorems for products of non-negative and tropical random matrices
Abstract: Tropical matrices are matrices with entries in $(\R\cup\{-\infty\}, \max,+)$, where $\max$ is seen as the “addition”. They appear as the limit of nonnegative matrices and in models from computer science/operations research, as they are strongly linked to weighted directed graphs. Their dynamical behavior is quite similar to nonnegative matrices, with a kind of Perron-Frobenius theorem but the limits are often reached, which allows some combinatorial studies. In this talk, I will present a common framework, known as topical maps, to deal with both nonnegative matrices...
Read MoreParametric rigidity of real families of conformal diffeomorphisms tangent to x -> -x
Abstract: We prove that one-parameter families of real germs of conformal diffeomorphisms tangent to the involution x -> -x are rigid in the parameter. We study the connection between the dynamics in the Poincar\’e and Siegel domains. Although repeatedly employed in the literature, the dynamics in the Siegel domain does not explain the intrinsic real properties of these germs. Rather, these properties are fully exploited in the Poincaré domain, where the fixed points are linearizable. However, a detailed study of the dynamics in the Siegel domain is of crucial importance. In this...
Read MoreFlujos geodésicos de superficies compactas sin puntos focales y genus mayor que 1 son extensiones de flujos expansivos.
Resumen: Demostramos que el flujo geodésico de una superficie compacta sin puntos focales de genus mayor que 1 es conjugado a un flujo expansivo en una variedad compacta por un homeomorfismo que preserva parámetro. Este flujo expansivo es rico en propiedades típicas de dinámica topológica hiperbólica: transitivo, órbitas periódicas densas, estructura de producto local, shadowing property. Y de acuerdo a la definición de extensión de un flujo expansivo adoptada por Sambarino, Vasquez, Buci et al, el flujo geodésico inicial resulta ser una extensión de dicho flujo expansivo. Aplicamos este...
Read MoreDynamical Cubes and a criteria for systems having product extensions
For a minimal$ Z^2-$topological dynamical systems, we introduce a cube structure and a generalization of the regionally proximal relation, which allow us to characterize product systems and their factors. We also introduce the concept of topological magic systems, which is the topological counterpart of measure theoretic magic systems introduced by Host in his study of multiple averages for commuting transformations. We give various applications of these structures, including the construction of some special factors in topological dynamics, and a computation of the automorphism group of...
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