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Every rational function can be naturally extended to a function whose ___domain and range are the whole [[Riemann sphere]] ([[complex projective line]]).
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 (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.
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