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ebsd2021:raissy [2021/04/26 17:06] – external edit 127.0.0.1ebsd2021:raissy [2021/10/25 08:07] (current) – tahzibi
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 +[[ebsd2021:participantsraissy|Comments and Questions of participants]]
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 +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
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 +[[ebsd2021:raissi1|Preliminares em Análise Complexa]]
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 +[[ebsd2021:raissi2|Mapas racionais na esfera de Riemann]]
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 +[[ebsd2021:raissi3|Teoria local: dinâmica perto de pontos periódicos]]
 +</WRAP>
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 +[[ebsd2021:raissi4|Teoria global: conjuntos de Julia e de Fatou e suas propriedades]]
 +</WRAP>
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 +[[ebsd2021:raissy5|Wandering domains for polynomials in higher dimension]]
 +</WRAP>
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 Discussions, Questions, Comments … Just write using latex commands (inside $$) in the following Discussion space and Save! Discussions, Questions, Comments … Just write using latex commands (inside $$) in the following Discussion space and Save!
  
 ~~DISCUSSION~~ ~~DISCUSSION~~
ebsd2021/raissy.1619467595.txt.gz · Last modified: 2021/04/26 17:06 by 127.0.0.1