[[ebsd2021:participantsraissy|Comments and Questions of participants]] The **tentative plan** of the minicourse is as follows:\\ 1- Introduction to parabolic Fatou components and the Leau-Fatou Flower Theorem in dimension 1\\ 2- Introduction to parabolic implosion in complex dimension 1\\ 3- Statement of the main result and begin of proof\\ 4 End of proof of main result and further developments\\ **References for the minicourse**: 1- M. Astorg, X. Buff, R. Dujardin, H. Peters and J. Raissy: //A two-dimensional polynomial mapping with a wandering Fatou component,// Ann. of Math. (2) 184 (2016), no. 1, 263--313, https://arxiv.org/pdf/1411.1188.pdf.\\ 2- E. Bedford, J. Smillie and T. Ueda: //Parabolic bifurcations in complex dimension 2//, Comm. Math. Phys. 350 (2017), no. 1, 1--29, https://arxiv.org/pdf/1208.2577.pdf\\ 3- X. Buff: //Wandering Fatou Component for Polynomials,// in KAWA Lectures Notes, Annales de la faculté des sciences de Toulouse, Ser. 6 (2018) 27/2, 445--475, http://www.numdam.org/item/10.5802/afst.1575.pdf\\ 4- A. Douady: //Does a Julia set depend continuously on the polynomial?// Complex dynamical systems (Cincinnati, OH, 1994), 91--138, Proc. Sympos. Appl. Math., 49, Amer. Math. Soc., Providence, RI, 1994\\ 5- D. Sullivan //Quasiconformal Homeomorphisms and Dynamics I. Solution of the Fatou-Julia Problem on Wandering Domains//, Ann. of Math. (2) 122 (1985), no. 3, 401--418, http://www.math.stonybrook.edu/~bishop/classes/math627.S13/Sullivan-1985-Nonwandering.pdf\\ **Prerequisites:**\\ 1- Basic complex analysis in dimension 1\\ 2- The Riemann sphere: its complex structures and the description of its group of holomorphic automorphisms\\ 3- Basic discrete holomorphic dynamics on the Riemann sphere: local theory\\ 4- Basic discrete holomorphic dynamics on the Riemann sphere: Fatou/Julia sets and their basic properties, statement of Fatou’s Classification of invariant Fatou Components, statement of Sullivan’s Non Wandering Theorem.\\ **Reference for the prerequisites (English)**\\ 1-Carne, Geometry and Groups https://www.dpmms.cam.ac.uk/~tkc/GeometryandGroups/GeometryandGroups.pdf\\ 2-Carleson and Gamelin, Complex Dynamics, https://zr9558.files.wordpress.com/2013/11/complex-dynamics-carleson.pdf\\ 3-Milnor, Dynamics in one complex variable, https://arxiv.org/pdf/math/9201272.pdf **Referencias para pre-requisitos (Português)**\\ Lomonaco, Notas de aulas, https://sites.google.com/view/lunalomonaco/teaching?authuser=0 [[ebsd2021:raissi1|Preliminares em Análise Complexa]] [[ebsd2021:raissi2|Mapas racionais na esfera de Riemann]] [[ebsd2021:raissi3|Teoria local: dinâmica perto de pontos periódicos]] [[ebsd2021:raissi4|Teoria global: conjuntos de Julia e de Fatou e suas propriedades]] [[ebsd2021:raissy5|Wandering domains for polynomials in higher dimension]] Discussions, Questions, Comments … Just write using latex commands (inside $$) in the following Discussion space and Save! ~~DISCUSSION~~