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--- ebsd2021:raissy [2021/10/24 21:15] – tahzibi
+++ ebsd2021:raissy [2021/10/25 08:07] (current) – tahzibi
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+<WRAP center round box 100%>
-====== Wandering domains for polynomials in higher dimension ======
+[[ebsd2021:participantsraissy|Comments and Questions of participants]]
+</WRAP>
-**Short abstract**: We will present the proof of the existence of a wandering domain for a polynomial endomorphism $\mathbb{C}^2$. The idea is to present the proof in such a way to emphasize the key steps in the construction and potential applications.
-**Extended abstract**: The filled-in Julia set $K_f$ of a polynomial map $f\colon\mathbb{C} \to \mathbb{C}$ is the set of points with bounded orbit under iteration of $f$. The Non Wandering Theorem proved by Sullivan in the 1980’s asserts that every connected component of the interior of $K_f$ is eventually periodic.
-The goal of the mini-course is to show that this result does not hold for polynomials maps $F\colon\mathbb{C}^2\to\mathbb{C}^2$. More precisely, we will show that if
-$$
-F(z,w)= \left(z - z^2, w + w^2 + aw^3 + {\pi^2\over 4} z \right)
-$$
-with $a < 1$ sufficiently close to $1$, then $F$ admits a wandering Fatou component.
-The proof uses techniques of parabolic implosion for skew-products. We will emphasize the key steps in the construction and give further developments and applications.\\
 The **tentative plan** of the minicourse is as follows:\\
 -  Introduction to parabolic Fatou components and the Leau-Fatou Flower Theorem in dimension 1\\
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-[[ebsd2021:raissi5|Wandering domains for polynomials in higher dimension]]
+[[ebsd2021:raissy5|Wandering domains for polynomials in higher dimension]]
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