## 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.

Full Text (PDF) [168 KB]

### Key words

discrete dynamical systems, polynomial maps, periodic points

37F10, 58F, 13P

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