Bifurcations of Periodic Points of Some Algebraic Maps

Abstract.

We study the local dynamics of maps $f(z) = -z -{\sum^{{\infty}}_{k=1}}\alpha_{k}z^{k+1},$ where f(z) is an irreducible branch of the algebraic curve

$$z+w+\mathop {\sum\limits_{i+j=n}}a_{ij}z^{i}w^{j}=0.$$

We give the complete description of bifurcations of 2-periodic points of f(z) in a small neighborhood of the origin when n is odd. For the case of even n some partial results regarding to the bifurcations of such points are obtained.