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In mathematics, the no-wandering-domain theorem is a result on dynamical systems, proven by Dennis Sullivan in 1985. The theorem states that a rational map ''f'' : Ĉ → Ĉ with deg(''f'') ≥ 2 does not have a wandering domain, where Ĉ denotes the Riemann sphere. More precisely, for every component ''U'' in the Fatou set of ''f'', the sequence : will eventually become periodic. Here, ''f'' ''n'' denotes the ''n''-fold iteration of ''f'', that is, : The theorem does not hold for arbitrary maps; for example, the transcendental map has wandering domains. However, the result can be generalized to many situations where the functions naturally belong to a finite-dimensional parameter space, most notably to transcendental entire and meromorphic functions with a finite number of singular values. ==References== * Lennart Carleson and Theodore W. Gamelin, ''Complex Dynamics'', Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993, ISBN 0-387-97942-5 * Dennis Sullivan, ''Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains'', Annals of Mathematics 122 (1985), no. 3, 401–18. * S. Zakeri, ''(Sullivan's proof of Fatou's no wandering domain conjecture )'' 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「No-wandering-domain theorem」の詳細全文を読む スポンサード リンク
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