Fixed points and orbits in skew polynomial rings

Adam Chapman, Elad Paran

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study orbits and fixed points of polynomials in a general skew polynomial ring D[x,σ,δ]. We extend results of the first author and Vishkautsan on polynomial dynamics in D[x]. In particular, we show that if a ∈D and f ∈ D[x,σ,δ] satisfy f(a) = a, then fon(a) = a for every formal power of f. More generally, we give a sufficient condition for a point a to be r-periodic with respect to a polynomial f. Our proofs build upon foundational results on skew polynomial rings due to Lam and Leroy.

Original languageEnglish
Article number2450078
JournalJournal of Algebra and its Applications
DOIs
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2024 World Scientific Publishing Company.

Keywords

  • Skew polynomials
  • arithmetic dynamics
  • division rings
  • noncommutative algebra
  • periodic points

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