On the Ergodic Theory of Tanaka–Ito Type $\alpha$-continued Fractions

Hitoshi Nakada, Wolfgang Steiner

Type: Article

Publication Date: 2021-08-26

Citations: 2

DOI: https://doi.org/10.3836/tjm/1502179343

Abstract

We show the ergodicity of Tanaka-Ito type $α$-continued fraction maps and construct their natural extensions. We also discuss the relation between entropy and the size of the natural extension domain.

Locations

arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
DataCite API - View
Tokyo Journal of Mathematics - View

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Works Cited by This (8)

Action	Title	Year	Authors
+	Bernoulli maps of the interval	1977	Rufus Bowen
+ PDF Chat	Metrical Theory for a Class of Continued Fraction Transformations and Their Natural Extensions	1981	Hitoshi Nakada
+ PDF Chat	On a Family of Continued-Fraction Transformations and Their Ergodic Properties	1981	Shunji Ito Shigeru Tanaka
+ PDF Chat	A Note on the Ergodic Theorem of Information Theory	1961	Kai Lai Chung
+ PDF Chat	Some remarks on ergodicity and invariant measures.	1975	Fritz Schweiger
+	SOME STRONG MIXING PROPERTIES OF A SEQUENCE OF RANDOM VARIABLES ARISING FROM α-CONTINUED FRACTIONS	2003	Hitoshi Nakada Rie Natsui
+	Ergodic properties of infinite measure-preserving interval maps with indifferent fixed points	2000	Roland Zweimüller
+ PDF Chat	Natural extensions and entropy of<i>α</i>-continued fractions	2012	Cor Kraaikamp Thomas Schmidt Wolfgang Steiner