| Title: | Parameterized family of annular homeomorphisms with pseudo-circle attractors |
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| Authors: | ID Činč, Jernej (Author)
ID Oprocha, Piotr (Author) |
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| Files: |  RAZ_Cinc_Jernej_2024.pdf (514,64 KB)
MD5: CFF5CFA149983435C954550E1A3124ED
 https://doi.org/10.1016/j.jde.2024.06.008
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | In this paper we construct a paramaterized family of annular homeomorphisms with Birkhoff-like rotational attractors that vary continuously with the parameter, are all homeomorphic to a unique topological object, called the R.H. Bing's pseudo-circle, yet display an interesting boundary dynamics. Namely, in the
constructed family of homeomorphisms the outer prime ends rotation number vary continuously with the parameter through the interval [0, 1/2]. This, in particular, answers a question from Boroński et al. (2020) [15]. Furthermore, these attractors preserve the induced Lebesgue measure from the circle and have strong
measure-theoretic and statistical properties. To show main results of the paper we first prove a result of an independent interest, that Lebesgue-measure preserving circle maps generically satisfy the crookedness condition which implies that generically the inverse limits of Lebesgue measure-preserving circle maps are
the pseudo-solenoids. For degree one circle maps, this implies that the generic inverse limit in this context
is the pseudo-circle. |
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| Keywords: | Lebesgue measure, circle maps, pseudo-circle, Brown-Barge-Martin embeddings, strange attractors |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 17.11.2023 |
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| Article acceptance date: | 05.06.2024 |
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| Publication date: | 21.06.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 102-132 |
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| Numbering: | Letn. 407 |
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| PID: | 20.500.12556/DKUM-89364  |
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| UDC: | 517.987 |
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| ISSN on article: | 0022-0396 |
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| COBISS.SI-ID: | 200659459 |
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| DOI: | 10.1016/j.jde.2024.06.008 |
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| Publication date in DKUM: | 26.02.2025 |
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| Views: | 138 |
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| Downloads: | 16 |
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| Metadata: |    |
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| Categories: | Misc.
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