Volume 27, pp. 156-162, 2007.

Periodic points of some algebraic maps

Valery G. Romanovski

Abstract

We study the local dynamics of maps f(z)=zn=1αnzn+1, where f(z) is an irreducible branch of the algebraic curve z+w+i+j=naijziwj=0. We show that the center and cyclicity problems have simple solutions when n is odd. For the case of even n some partial results are obtained.

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Key words

discrete dynamical systems, polynomial maps, periodic points

AMS subject classifications

37F10, 58F, 13P