Continued fractions with two non integer digits

Abstract: In this talk, we will look at a family of continued fraction expansions for which the digits in the expansions can attain two different (typically non-integer) values, named $\alpha_1$ and $\alpha_2$ with $\alpha_1 \alpha_2 \le 1/2$. If $\alpha_1 \alpha_2 < 1/2$ we can associate a dynamical system to these expansions with a switch region and therefore with lazy and greedy expansions. We will explore the parameter space and highlight certain values for which we can construct the natural extension (such as a family for which the lowest digit cannot be followed by itself). We end the talk with a list of open problems.

dynamical systemsnumber theory

Audience: researchers in the topic

( slides )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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