Women in Dynamical Systems & Ergodic Theory
timetable:
Tue 21 May, 17:00 - 17:30, Aula Dini
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Non-winning Bad Subsets
speaker: Dorsa Hatefi (University of York)abstract: It is well known that the set of badly approximable numbers (real numbers with bounded continued fraction elements), which we denote as Bad, has zero Lebesgue measure yet full Hausdorff dimen- sion(Jarnik 1928). In fact, it fulfills the stronger property of being a winning set in the sense of Schmidt’s Game(1966). It has also been shown that the set of inhomogeneously badly approximable numbers, Bad(γ) is full dimension(2015). We prove that Bad(γ) \ Bad, i.e. the inhomogeneous set independent of Bad is also full dimension. Since this set cannot be winning, this is done via introducing a variant of the Schmidt game which we call the rapid game, played on the space of unimodular grids.
timetable:
Tue 21 May, 17:00 - 17:30, Aula Dini
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