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Generic point equivalence and Pisot numbers
- Authors
- Akiyama, Shigeki; Kaneko, Hajime; Kim, Dong Han
- Issue Date
- Dec-2020
- Publisher
- CAMBRIDGE UNIV PRESS
- Keywords
- normal number; beta expansion; generic point; Pisot number
- Citation
- ERGODIC THEORY AND DYNAMICAL SYSTEMS, v.40, no.12, pp 3169 - 3180
- Pages
- 12
- Indexed
- SCIE
SCOPUS
- Journal Title
- ERGODIC THEORY AND DYNAMICAL SYSTEMS
- Volume
- 40
- Number
- 12
- Start Page
- 3169
- End Page
- 3180
- ISSN
- 0143-3857
1469-4417
- Abstract
- Let beta > 1 be an integer or, generally, a Pisot number. Put T (x) = {beta x} on [0, 1] and let S : [0; 1] -> [0, 1] be a piecewise linear transformation whose slopes have the form +/- beta(m) with positive integers m. We give a sufficient condition for T and S to have the same generic points. We also give an uncountable family of maps which share the same set of generic points.
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Related Researcher
- Kim, Dong Han
- College of Education (Department of Mathematics Education)