$\alpha$-odd continued fractions

Claire Merriman (Ohio State University)

05-Jan-2021, 13:30-14:30 (3 years ago)

Abstract: The standard continued fraction algorithm come from the Euclidean algorithm. We can also describe this algorithm using a dynamical system of $[0,1)$, where the transformation that takes $x$ to the fractional part of $1/x$ is said to generate the continued fraction expansion of $x$. From there, we ask two questions: What happens to the continued fraction expansion when we change the domain to something other than $[0,1)$? What happens to the dynamical system when we impose restrictions on the continued fraction expansion, such as finding the nearest odd integer instead of the floor? This talk will focus on the case where we first restrict to odd integers, then start shifting the domain $[\alpha-2, \alpha)$. This talk is based on joint work with Florin Boca and animations done by Xavier Ding, Gustav Jennetten, and Joel Rozhon as part of an Illinois Geometry Lab project.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )


One World Numeration seminar

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*
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