Julia sets for a class of polynomial maps in R^2 and C^2 – Danilo Caprio

Danilo Caprio
I2M, Aix-Marseille Université

Date(s) : 10/05/2019   iCal
11 h 00 min - 12 h 00 min

In this lecture we consider a class of endomorphisms of $\mathbb{R}^2$ defined by $f(x,y)=(xy+c,x)$, where $c\in\mathbb{R}$ is a real number and we prove that when $-1<c<0$, the forward filled Julia set of $f$ is the union of stable manifolds of fixed and $3-$periodic points of $f$. Furthermore, we prove that the backward filled Julia set of $f$ is the union of unstable manifolds of the saddle fixed and $3-$periodic points of $f$.
We also study the dynamics of the family $f_{c,d}(x, y) = (xy+c, x+d)$ of endomorphisms of $\mathbb{C}^2$, where $c$ and $d$ are complex parameters with $|d|<1$.





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