Actions of linearized polynomials on the algebraic closure of a finite field

  • Let g and h be monic polynomials in F[x], where F is the finite field of order q. We define a dynamical system by letting the q-linearized polynomial associated with g act on equivalence classes of a certain F-subspace of the algebraic closure of F in which related elements of the closure lie in the same orbit under the action of the q-linearized polynomial associated with h. When h = x, this is equivalent to the system in which the dynamic polynomial g acts on irreducible polynomials over F as discussed in [CH], where a conjecture of Morton [M] was proved as regards linearized polynomials. A generalization of that result is proved here. This states that when g and h are non-constant relatively prime polynomials, then there are infinitely many classes with prescribed preperiod and primitive period in the (g,h)-dynamical system.

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Metadaten
Author:Stephen D. Cohen, Dirk HachenbergerORCiDGND
URN:urn:nbn:de:bvb:384-opus4-8606
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1004
ISBN:978-0-8218-0817-7OPAC
Parent Title (English):Finite Fields: Theory, Applications and Algorithms; Fourth International Conference on Finite Fields: Theory, Applications, and Algorithms, August 12 - 15, 1997, University of Waterloo, Ontario, Canada
Publisher:American Mathematical Society
Place of publication:Providence, Rhode Island
Editor:Ronald C. Mullin, Gary L. Mullen
Type:Conference Proceeding
Language:English
Year of first Publication:1999
Publishing Institution:Universität Augsburg
Release Date:2008/06/19
Tag:linearized polynomials; algebraic closure; dynamical system; finite field
GND-Keyword:Dynamisches System; Abschließung; Galois-Feld; Polynom
First Page:17
Last Page:32
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Diskrete Mathematik, Optimierung und Operations Research
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik

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