ON A CLASS OF RAUZY FRACTALS WITHOUT THE FINITENESS PROPERTY

Pavani, Gustavo A.

doi:https://doi.org/10.18910/73358

アクセス数:62件（2024-04-24 11:27 集計）

固定URL: https://doi.org/10.18910/73358

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タイトル	ON A CLASS OF RAUZY FRACTALS WITHOUT THE FINITENESS PROPERTY
著者	著者名 Pavani, Gustavo A.
抄録	We present some topological and arithmetical aspects of a class of Rauzy fractals 𝓡_<𝑎,𝑏> related to the polynomials of the form 𝑷_<𝑎,𝑏>(𝑥) = 𝑥³ −𝑎𝑥² −𝑏𝑥−1, where a and b are integers satisfying −𝑎 + 1 ≤ 𝑏 ≤ −2. This class has the property that 0 lies on the boundary of 𝓡_<𝑎,𝑏>. We construct explicit finite automata that recognize the boundaries of these fractals. This allows to establish the number of neighbors of 𝓡_<𝑎,𝑏> in the tiling it generates. Furthermore, we prove tha if 2𝑎 + 3𝑏 + 4 ≤ 0 then 𝓡_<𝑎,𝑏> is not homeomorphic to a topological disk. We also show that the boundary of the set 𝓡_<₃,−₂> is generated by two infinite iterated function systems.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	56(3)
ページ	577-599
刊行年月	2019-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/73358
DOI	https://doi.org/10.18910/73358
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 56, Number 3 （2019-7）

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. 2019, 56(3), p. 577-599
DC.title	ON A CLASS OF RAUZY FRACTALS WITHOUT THE FINITENESS PROPERTY
DC.creator	Pavani, Gustavo A.
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	2019-07
DCTERMS.abstract	We present some topological and arithmetical aspects of a class of Rauzy fractals 𝓡_<𝑎,𝑏> related to the polynomials of the form 𝑷_<𝑎,𝑏>(𝑥) = 𝑥³ −𝑎𝑥² −𝑏𝑥−1, where a and b are integers satisfying −𝑎 + 1 ≤ 𝑏 ≤ −2. This class has the property that 0 lies on the boundary of 𝓡_<𝑎,𝑏>. We construct explicit finite automata that recognize the boundaries of these fractals. This allows to establish the number of neighbors of 𝓡_<𝑎,𝑏> in the tiling it generates. Furthermore, we prove tha if 2𝑎 + 3𝑏 + 4 ≤ 0 then 𝓡_<𝑎,𝑏> is not homeomorphic to a topological disk. We also show that the boundary of the set 𝓡_<₃,−₂> is generated by two infinite iterated function systems.
DC.identifier	10.18910/73358
DC.format	application/pdf
citation_title	ON A CLASS OF RAUZY FRACTALS WITHOUT THE FINITENESS PROPERTY
citation_author	Pavani, Gustavo A.
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2019-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	56
citation_issue	3
citation_firstpage	577
citation_lastpage	599
citation_public_url	https://hdl.handle.net/11094/73358
citation_doi_detail	10.18910/73358
citation_doi	https://doi.org/10.18910/73358

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