[Todos CMAT] Seminario de Sistemas Dinámicos - Gabriel Fuhrmann (Durham University)

[seminarios en cmat.edu.uy]

Seminario de Sistemas Dinámicos
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Título: "On the lack of equidistribution on fat Cantor sets"

Expositor: Gabriel Fuhrmann (Durham University)

Resumen:
 
Given an irrational rotation, it is straightforward to see that for every Cantor
set C, there is a dense set of points whose orbit doesn't intersect C. On the
other hand, if C is a fat Cantor set (that is, of positive Lebesgue measure),
almost every point visits C with a frequency equal to the measure of C. But what
other frequencies of visits to C may occur? In the words of a recent
MathOverflow post [1], what is the Birkhoff spectrum of fat Cantor sets?

We give a first answer to this question by showing that every irrational
rotation allows for certain fat Cantor sets C whose Birkhoff spectrum is
maximal, that is, equal to the interval [0,Leb(C)]. In this talk, I will focus
on discussing some of the basic tools behind this result and extensions of it.

[1] D. Kwietniak, Possible Birkhoff spectra for irrational rotations,
MathOverflow (2020), https://mathoverflow.net/q/355860 (version: 2020-03-27).
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Viernes 15/12 a las 14:30, Salón de seminarios del IMERL

Contacto: Santiago Martinchich - smartinchich en cmat.edu.uy
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El seminario será transmitido por el siguiente link si alguien manifiesta
interés de que así ocurra hasta el día antes del seminario: https://salavirtual-
udelar.zoom.us/j/83020032334?pwd=djAxdmg2K3NDVEU0V3RZSXkxNW8xUT09
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Más seminarios en: http://www.cmat.edu.uy/seminarios
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