Dear all,

We are having our first online seminar this Thursday. The details are

Speaker: Erik Contreras, PUC Santiago
Title: k-rational approximations in k-luroth expansions
Date and time: 16th April 2pm
Online link: https://bluejeans.com/287667352

Please turn your microphone and camera off when you join. If you have a question during the talk please either turn on your microphone or put a comment in the chat.

Abstract:
Given an irrational number, one can think about the speed of approximation by rationals. The speed of approximation depends on the expansion that we expand the numbers. Examples of typical expansions are the numerical systems generated by continued fractions, as well as base b expansions. In this talk, we are interested in a one-parameter family of numerical systems called k-Lüroth expansions, each one generated by an interval map $L_k$. Each k-Lüroth expansion allows us to consider k-rationals and irrational numbers of [0,1]. In particular we are interested in the size of numbers in [0,1] having the same exponential speed of approximations by $k$-rationals, for different values of $k$. With this un mind, we will show that the Hausdorff dimension of these sets varies analytically with respect to the parameter $k$ using tools from thermodynamic formalism for countable Markov shifts.

Best wishes,

Thomas


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