Noticias en español
Parametric 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...
Read MoreBlock Maps between Primitive Uniform and Pisot Substitutions
Abstract: We prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an element of this set, up to a shift. This result is proved using a common generalization of block maps and substitutions, which we call dill maps.
Read MorePlaying with Subshifts
Abstract: We study the class of word-building games, where two players pick letters from afinite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player A) or not (a win for player B). We focus on symbolic dynamical games, where the target set is a subshift. We investigate the relation between the target subshift and the set of turn orders for which A has a winning strategy.
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