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.
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Romanovski, V.G. Bifurcations of Periodic Points of Some Algebraic Maps. Math.comput.sci. 1, 253–265 (2007). https://doi.org/10.1007/s11786-007-0017-3
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DOI: https://doi.org/10.1007/s11786-007-0017-3