Hausdorff dimension of Gauss-Cantor sets and their applications to the study of classical Markov spectrum
Polina Vytnova (University of Warwick)
Abstract: The classical Lagrange and Markov spectra are subsets of the real line which arise in connection with some problems in theory Diophantine approximation theory. In 1921 O. Perron gave a definition in terms of continued fractions, which allowed to study the Markov and Lagrange spectra using limit sets of iterated function schemes.
In this talk we will see how the first transition point, where the Markov spectra acquires the full measure can be computed by the means of estimating Hausdorff dimension of the certain Gauss-Cantor sets.
The talk is based on a joint work with C. Matheus, C. G. Moreira and M. Pollicott.
dynamical systemsnumber theory
Audience: researchers in the topic
( slides )
Series comments: Description: Online seminar on numeration systems and related topics
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| Organizers: | Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner* |
| *contact for this listing |