Degree growth, linear independence and periods of a class of rational dynamical systems

Alina Ostafe*, Igor Shparlinski

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well as about possible lengths of trajectories generated by such dynamical systems over finite fields. Some of these results are generalisations of those known in the polynomial case, some are new even in this case.

Original languageEnglish
Title of host publicationArithmetic, geometry, cryptography and coding theory
Subtitle of host publication13th Conference [on] Arithmetic, Geometry, Cryptography and Coding Theory, CIRM, Marseille, France, March 14-18, 2011 : Geocrypt 2011, Bastia, France, June 19-24, 2011
EditorsY Aubry, C Ritzenthaler, A Zykin
Place of PublicationProvidence
PublisherAmerican Mathematical Society
Pages131-143
Number of pages13
ISBN (Print)9780821875728
DOIs
Publication statusPublished - 2012
Event13th Conference Arithmetic, Geometry, Cryptography and Coding Theory - Marseille, France
Duration: 14 Mar 201118 Mar 2011

Publication series

NameContemporary Mathematics
PublisherAMER MATHEMATICAL SOC
Volume574
ISSN (Print)0271-4132

Conference

Conference13th Conference Arithmetic, Geometry, Cryptography and Coding Theory
CountryFrance
CityMarseille
Period14/03/1118/03/11

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