Rational function: Difference between revisions

Revision as of 07:42, 14 January 2025

Revision as of 08:43, 14 January 2025

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Rational functions are representative examples of [[meromorphic function]]s.<ref>{{cite book | last=Ablowitz | first=Mark J. | author1-link = Mark Ablowitz | last2=Fokas | first2=Athanassios S. | author2-link=Athanassios Fokas | title=Complex Variables | publisher=Cambridge University Press | date=2003 | isbn=978-0-521-53429-1|p=150}}</ref>

Iteration of rational functions on the [[Riemann sphere]] (i.e. a [[rational mapping]]) creates [[discrete dynamical system]]s.<ref>{{cite journal | last=Blanchard | first=Paul | title=Complex analytic dynamics on the Riemann sphere | journal=Bulletin of the American Mathematical Society | volume=11 | issue=1 | date=1984 | issn=0273-0979 | doi=10.1090/S0273-0979-1984-15240-6 | doi-access=free | pages=85–141|url=https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-11/issue-1/Complex-analytic-dynamics-on-the-Riemann-sphere/bams/1183551835.full}} p. 87</ref>

Iteration of rational functions (maps)<ref>{{cite web |url=https://www.matem.unam.mx/~omar/no-wandering-domains.pdf |title=Iteration of Rational Functions |first=Omar Antolín |last=Camarena}}</ref> on the [[Riemann sphere]] creates [[discrete dynamical system]]s.

===Notion of a rational function on an algebraic variety===