AN ENTROPY PROBLEM OF THE α-CONTINUED FRACTION MAPS

Nakada, Hitoshi

Osaka Journal of Mathematics, 2022, 59(2), 453-464

アクセス数:120件（2025-07-12 00:24 集計）

固定URL: https://doi.org/10.18910/87487

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タイトル	AN ENTROPY PROBLEM OF THE α-CONTINUED FRACTION MAPS
著者	NRID 1000040118980 1000040118980 著者名 Nakada, Hitoshi
抄録	We show that the entropy of the α-continued fraction map w.r.t the absolutely continuous invariant probability measure is strictly less than that of the nearest integer continued fraction map when 0 < α < (3−√5) / 2 . This answers a question by C. Kraaikamp, T. A. Schmidt, and W. Steiner (2012). To prove this result we make use of the notion of the geodesic continued fractions introduced by A. F. Beardon, M. Hockman, and I. Short (2012).
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	59(2)
ページ	453-464
刊行年月	2022-04
言語	英語
ハンドルURL	https://hdl.handle.net/11094/87487
DOI	https://doi.org/10.18910/87487
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 59, Number 2 （2022-4）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2022, 59(2), p. 453-464
DC.title	AN ENTROPY PROBLEM OF THE α-CONTINUED FRACTION MAPS
DC.creator	Nakada, Hitoshi
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2022-04
DCTERMS.abstract	We show that the entropy of the α-continued fraction map w.r.t the absolutely continuous invariant probability measure is strictly less than that of the nearest integer continued fraction map when 0 < α < (3−√5) / 2 . This answers a question by C. Kraaikamp, T. A. Schmidt, and W. Steiner (2012). To prove this result we make use of the notion of the geodesic continued fractions introduced by A. F. Beardon, M. Hockman, and I. Short (2012).
DC.identifier	10.18910/87487
DC.format	87487
citation_title	AN ENTROPY PROBLEM OF THE α-CONTINUED FRACTION MAPS
citation_author	Nakada, Hitoshi
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2022-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	59
citation_issue	2
citation_firstpage	453
citation_lastpage	464
citation_public_url	https://hdl.handle.net/11094/87487
citation_doi_detail	10.18910/87487
citation_doi	https://doi.org/10.18910/87487