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)=-z-\sum_{n=1}^\infty \alpha_n z^{n+1}, $ where $f(z)$ is an irreducible branch of the algebraic curve $$ z+w+ \sum_{i+j=n}a_{ij} z^i w^j =0. $$ 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

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