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On periodic points under the iteration of additive polynomials

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Abstract.

Let F be a field and f(X) F[X]. An element P of F is called a (pre)periodic point of f if the sequence P, f(P), f(f(P)), … is (eventually) periodic. In the case where F is a function field of characteristic p>0 and f(X)=aX q+bX or f(X)=aX q 2+bX q+cX with q a power of p, we try to give effective upper bounds (depending only on q and F) for the number of (pre)periodic points of f in F.

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  1. Korea Institute for Advanced Study (KIAS), 207-43 Cheongnyangni 2-dong, Dongdaemun-gu Seoul, 130-722, Korea

    Andreas Schweizer

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  1. Andreas Schweizer
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Correspondence to Andreas Schweizer.

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Mathematics Subject Classification (2000): primary: 11C08, secondary: 11G09, 37E15

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Schweizer, A. On periodic points under the iteration of additive polynomials. manuscripta math. 113, 25–34 (2004). https://doi.org/10.1007/s00229-003-0419-8

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  • DOI: https://doi.org/10.1007/s00229-003-0419-8

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