Noticias en español
Open dynamics on subshifts of finite type.
RESUMEN: Dynamical systems can be broadly classified into closed and open systems. In a (traditional) closed system, the orbit of a point lies in the state space for all time, whereas in an open system, the orbit of a point may eventually escape from the state space through a hole. The notion of open dynamical systems was introduced by Pianigiani and Yorke in 1979, motivated by the dynamics of a ball on a billiard table with pockets. It has attracted the attention of researchers since then especially due to its wide applications.
Read MoreAcciones Evanescentes Aunque Recurrentes.
RESUMEN En los años 60, Edelstein dio ejemplos de isometrías afines sin punto fijo de espacios de Hilbert para las cuales una sucesión de iterados converge a la identidad. Este fenómeno no puede producirse en dimensión finita, incluso para métricas no hilbertianas. En esta charla veremos que ejemplos del tipo de Edelstein aparecen naturalmente asociadas a dinámicas clásicas sobre ciertos espacios. La charla girará en torno a la reciente prepublicación https://arxiv.org/pdf/2501.12120; se presentarán varios problemas abiertos y eventuales direcciones de investigación.
Read MoreIntrinsic ergodicity for a certain class of Derived from Anosov.
RESUMEN: We will talk briefly about some classic examples of Derived from Anosov (DA), that is, homotopic maps to an Anosov diffeomorphism, whose dynamics are partially hyperbolic. We will address some known results related to entropy invariance and the existence (and uniqueness) of measures of maximal entropy for this class of diffeomorphisms. Finally, we will present recent results in collaboration with L. Parra (PUCV) and C. Vásquez (PUCV) for a certain class of DA generated after a Hopf bifurcation, previously introduced by [M. Carvalho’93].
Read MoreComplexities of words generated by a billiard in the hypercube.
RESUMEN: Sturmian words form a class of binary infinite words which sheds light, through its equivalent definitions, on remarkable interactions between combinatorics, dynamical systems, and number theory. They give rise to several generalizations over the d-letter alphabet, for d ≥ 3. A large program, initiated in the 80s, is to determine which characteristic properties of Sturmian words each of these generalizations still satisfy. My talk will focus on one dynamical representations of Sturmian words: as words generated by a billiard on a square table, which generalizes itself to a billiard...
Read MoreAperiodic Wang tiles associated with metallic means.
RESUMEN: A Penrose tiling consists of two polygonal tiles whose frequency ratio is equal to the golden ratio. Similarly, tilings by the aperiodic monotile discovered in 2023 by David Smith are such that the ratio of the frequencies of the two orientations of the monotile is equal to the fourth power of the golden ratio. The structure of Jeandel-Rao tilings discovered in 2015 is also explained using the golden ratio. We know of aperiodic tilings that are not related to the golden ratio. However, the characterization of possible numbers for such ratios is a question, posed as early as 1992 by...
Read MoreCondiciones para la inestabilidad estructural de contracciones a trozos del intervalo.
RESUMEN: En la presente charla mostraremos que, bajo condiciones razonables, los mapas contractivos a trozos del intervalo que admiten dinámicas asintóticas no-periódicas no pueden ser estructuralmente estables. Se mencionarán algunos obstáculos y preguntas que surgieron durante este trabajo, tales como: ¿qué tipo de perturbaciones o topología deberíamos considerar? ¿cómo controlamos que las perturbaciones de contracciones a trozos sean contractivas a trozos sin exigir hipótesis adicionales? Dado que varios resultados críticos para esta demostración no dependen de la “contracción a...
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