Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
