Generic point equivalence and Pisot numbers

S. Akiyama; H. Kaneko; D. Han Kim

doi:10.1017/etds.2019.46

Generic point equivalence and Pisot numbers

S. Akiyama
, H. Kaneko
, D. Han Kim

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let 1]]> be an integer or, generally, a Pisot number. Put on and let be a piecewise linear transformation whose slopes have the form with positive integers. We give a sufficient condition for and to have the same generic points. We also give an uncountable family of maps which share the same set of generic points.

Original language	English
Pages (from-to)	3169-3180
Number of pages	12
Journal	Ergodic Theory and Dynamical Systems
Volume	40
Issue number	12
DOIs	https://doi.org/10.1017/etds.2019.46
State	Published - 1 Dec 2020

Keywords

11K16 (Secondary)
37E05 (Primary)
beta expansion
generic point
normal number
Pisot number 2010 Mathematics Subject Classification

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10.1017/etds.2019.46

Cite this

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title = "Generic point equivalence and Pisot numbers",

abstract = "Let 1]]> be an integer or, generally, a Pisot number. Put on and let be a piecewise linear transformation whose slopes have the form with positive integers. We give a sufficient condition for and to have the same generic points. We also give an uncountable family of maps which share the same set of generic points.",

keywords = "11K16 (Secondary), 37E05 (Primary), beta expansion, generic point, normal number, Pisot number 2010 Mathematics Subject Classification",

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AU - Han Kim, D.

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AB - Let 1]]> be an integer or, generally, a Pisot number. Put on and let be a piecewise linear transformation whose slopes have the form with positive integers. We give a sufficient condition for and 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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KW - 37E05 (Primary)

KW - beta expansion

KW - generic point

KW - normal number

KW - Pisot number 2010 Mathematics Subject Classification

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JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 12

ER -

Generic point equivalence and Pisot numbers

Abstract

Keywords

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