Representations of real numbers on fractal sets

Kan Jiang (Ningbo University)

13-Oct-2020, 12:30-13:30 (3 years ago)

Abstract: There are many approaches which can represent real numbers. For instance, the $\beta$-expansions, the continued fraction and so forth. Representations of real numbers on fractal sets were pioneered by H. Steinhaus who proved in 1917 that $C+C=[0,2]$ and $C−C=[−1,1]$, where $C$ is the middle-third Cantor set. Equivalently, for any $x \in [0,2]$, there exist some $y,z \in C$ such that $x=y+z$. In this talk, I will introduce similar results in terms of some fractal sets.

dynamical systemsnumber theory

Audience: researchers in the topic

( 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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