User Tools

Site Tools


ebsd2021:raissy

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision
Previous revision
ebsd2021:raissy [2021/08/31 14:25] escolaebsd2021:raissy [2021/10/25 08:07] (current) tahzibi
Line 1: Line 1:
-Aqui vamos escrever o material $f(z)= z^2 + c$ 
  
- +<WRAP center round box 100%> 
-<WRAP center round box 60%> +[[ebsd2021:participantsraissy|Comments and Questions of participants]]
-Tema 1+
 </WRAP> </WRAP>
 +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\\
  
-<WRAP center round box 60%> +**References for the minicourse**: 
-Tema + 
-</WRAP>+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
  
 <WRAP center round box 60%> <WRAP center round box 60%>
-Tema 3+[[ebsd2021:raissi1|Preliminares em Análise Complexa]]
 </WRAP> </WRAP>
  
 <WRAP center round box 60%> <WRAP center round box 60%>
-Tema 4+[[ebsd2021:raissi2|Mapas racionais na esfera de Riemann]]
 </WRAP> </WRAP>
  
 <WRAP center round box 60%> <WRAP center round box 60%>
-Tema 5+[[ebsd2021:raissi3|Teoria local: dinâmica perto de pontos periódicos]]
 </WRAP> </WRAP>
  
 <WRAP center round box 60%> <WRAP center round box 60%>
-Tema 6+[[ebsd2021:raissi4|Teoria global: conjuntos de Julia e de Fatou e suas propriedades]]
 </WRAP> </WRAP>
- 
 <WRAP center round box 60%> <WRAP center round box 60%>
-Tema 7+[[ebsd2021:raissy5|Wandering domains for polynomials in higher dimension]]
 </WRAP> </WRAP>
- 
- 
  
 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.1630430702.txt.gz · Last modified: 2021/08/31 14:25 by escola