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- Title
Fixed points and orbits in skew polynomial rings.
- Authors
Chapman, Adam; Paran, Elad
- 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 f ∘ n (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.
- Subjects
POLYNOMIAL rings; ORBITS (Astronomy); NONCOMMUTATIVE algebras; DIVISION rings; POLYNOMIALS
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 8, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498824500786