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Transitive actions and purely periodic N-expansions.

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Title: Transitive actions and purely periodic N-expansions.
Authors: Javaheri, Mohammad1 (AUTHOR) mjavaheri@siena.edu
Source: Journal of Number Theory. Jun2026, Vol. 283, p1-14. 14p.
Subjects: Semigroups (Algebra), Rational numbers, Dynamical systems, System dynamics
Abstract: We study the dynamical properties of the semigroup 〈 f , g 〉 generated by the maps f (x) = x + 1 and g (x) = N / x acting on the positive rational numbers Q + , with a focus on their connection to N -expansions. For N ∈ N ∖ { 1 , 2 , 3 , 4 , 6 } , we establish the existence of an infinite subset A ⊆ Q + on which 〈 f , g 〉 acts transitively: for any x , y ∈ A , there exists σ ∈ 〈 f , g 〉 such that y = σ (x). We use this result to show that, for the same values of N , there are infinitely many rational numbers with purely periodic N -expansions of any sufficiently large minimal period. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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AccessLevel: 6
PubType: Academic Journal
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  Data: Transitive actions and purely periodic N-expansions.
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  Data: <searchLink fieldCode="AR" term="%22Javaheri%2C+Mohammad%22">Javaheri, Mohammad</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mjavaheri@siena.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Jun2026, Vol. 283, p1-14. 14p.
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  Data: We study the dynamical properties of the semigroup 〈 f , g 〉 generated by the maps f (x) = x + 1 and g (x) = N / x acting on the positive rational numbers Q + , with a focus on their connection to N -expansions. For N ∈ N ∖ { 1 , 2 , 3 , 4 , 6 } , we establish the existence of an infinite subset A ⊆ Q + on which 〈 f , g 〉 acts transitively: for any x , y ∈ A , there exists σ ∈ 〈 f , g 〉 such that y = σ (x). We use this result to show that, for the same values of N , there are infinitely many rational numbers with purely periodic N -expansions of any sufficiently large minimal period. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jnt.2025.11.013
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 1
    Subjects:
      – SubjectFull: Semigroups (Algebra)
        Type: general
      – SubjectFull: Rational numbers
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: System dynamics
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      – TitleFull: Transitive actions and purely periodic N-expansions.
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            – D: 01
              M: 06
              Text: Jun2026
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              Y: 2026
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              Value: 283
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