Seminari di Sistemi Dinamici Olomorfi 2017-2018
timetable:
Wed 22 Nov, 16:30 - 17:30, Sala Conferenze Centro De Giorgi
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seminar: On the fractal geometry of the Lagrange and Markov spectra
speaker: Carlos Matheus Silva Santos ( CNRS)abstract: After the remarkable works of Markov in 1879 and 1880, the Lagrange and Markov spectra (coding arithmetic properties of irrational numbers and indefinite binary quadratic forms) were studied by several authors (including Perron, Hall, Freiman, Cusick, Flahive, ...).
In this talk, we will discuss the complement of the Lagrange spectrum L in the Markov spectrum M. More precisely, after recalling the results of Freiman, Cusick and Flahive from the 70's and 80's showing that M\L contains a countable, infinite subset, we will show that the Hausdorff dimension of M\L is strictly between 0 and 1.
timetable:
Wed 22 Nov, 16:30 - 17:30, Sala Conferenze Centro De Giorgi
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