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Computational Methods and Function Theory 8 (2008), No. 1, 101--106
Copyright Heldermann Verlag 2008

Permutable Entire Functions Satisfying Algebraic Differential Equations

Walter Bergweiler
bergweiler@math.uni-kiel.de , Christian-Albrechts-Universität zu Kiel, Mathematisches Seminar, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany.

[Abstract-pdf] [Abstract-ps]

We show that if f and g are transcendental entire functions such that f(g)=g(f), then f satisfies an algebraic differential equation if and only if g does.

Keywords: Permutable, commuting, iteration, factorization, differential equation.

MSC 2000: Primary 30D05; Secondary 34M05, 39B12.

[FullText-pdf (221 K)] [FullText-ps (375 K)]