Quantitative recurrence and the shrinking target problem for overlapping iterated function systems Article Swipe
Simon Baker
,
Henna Koivusalo
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.aim.2024.109538
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.aim.2024.109538
In this paper we study quantitative recurrence and the shrinking target problem for dynamical systems coming from overlapping iterated function systems. Such iterated function systems have the important property that a point often has several distinct choices of forward orbit. As is demonstrated in this paper, this non-uniqueness leads to different behaviour to that observed in the traditional setting where every point has a unique forward orbit. We prove several almost sure results on the Lebesgue measure of the set of points satisfying a given recurrence rate, and on the Lebesgue measure of the set of points returning to a shrinking target infinitely often. In certain cases, when the Lebesgue measure is zero, we also obtain Hausdorff dimension bounds. One interesting aspect of our approach is that it allows us to handle targets that are not simply balls, but may have a more exotic geometry.
Related Topics
Concepts
Iterated function system
Mathematics
Lebesgue measure
Iterated function
Measure (data warehouse)
Hausdorff measure
Orbit (dynamics)
Uniqueness
Function (biology)
Set (abstract data type)
Lebesgue integration
Dimension (graph theory)
Pure mathematics
Hausdorff dimension
Discrete mathematics
Mathematical analysis
Fractal
Computer science
Evolutionary biology
Database
Biology
Aerospace engineering
Engineering
Programming language
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.aim.2024.109538
- OA Status
- hybrid
- Cited By
- 2
- References
- 42
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4392329141
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4392329141Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1016/j.aim.2024.109538Digital Object Identifier
- Title
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Quantitative recurrence and the shrinking target problem for overlapping iterated function systemsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-02-29Full publication date if available
- Authors
-
Simon Baker, Henna KoivusaloList of authors in order
- Landing page
-
https://doi.org/10.1016/j.aim.2024.109538Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1016/j.aim.2024.109538Direct OA link when available
- Concepts
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Iterated function system, Mathematics, Lebesgue measure, Iterated function, Measure (data warehouse), Hausdorff measure, Orbit (dynamics), Uniqueness, Function (biology), Set (abstract data type), Lebesgue integration, Dimension (graph theory), Pure mathematics, Hausdorff dimension, Discrete mathematics, Mathematical analysis, Fractal, Computer science, Evolutionary biology, Database, Biology, Aerospace engineering, Engineering, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
- Citations by year (recent)
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2025: 2Per-year citation counts (last 5 years)
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42Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| corresponding_author_ids | https://openalex.org/A5061943510, https://openalex.org/A5077453606 |
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