ebsd2021:raissy
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| ebsd2021:raissy [2021/08/31 14:25] – escola | ebsd2021:raissy [2021/10/25 08:07] (current) – tahzibi | ||
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| - | Aqui vamos escrever o material $f(z)= z^2 + c$ | ||
| - | + | <WRAP center round box 100%> | |
| - | <WRAP center round box 60%> | + | [[ebsd2021: |
| - | Tema 1 | + | |
| </ | </ | ||
| + | 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 2 | + | |
| - | </WRAP> | + | 1- M. Astorg, X. Buff, R. Dujardin, H. Peters and J. Raissy: //A two-dimensional polynomial mapping with a wandering Fatou component,// |
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| + | 2- E. Bedford, J. Smillie and T. Ueda: //Parabolic bifurcations in complex dimension 2//, Comm. Math. Phys. 350 (2017), no. 1, 1--29, https:// | ||
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| + | 3- X. Buff: //Wandering Fatou Component for Polynomials,// | ||
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| + | 4- A. Douady: //Does a Julia set depend continuously on the polynomial?// | ||
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| + | 5- D. Sullivan // | ||
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| + | **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.\\ | ||
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| + | **Reference for the prerequisites (English)**\\ | ||
| + | 1-Carne, Geometry and Groups https:// | ||
| + | 2-Carleson and Gamelin, Complex Dynamics, https:// | ||
| + | 3-Milnor, Dynamics in one complex variable, https:// | ||
| + | |||
| + | **Referencias para pre-requisitos (Português)**\\ | ||
| + | Lomonaco, Notas de aulas, https:// | ||
| <WRAP center round box 60%> | <WRAP center round box 60%> | ||
| - | Tema 3 | + | [[ebsd2021: |
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| - | Tema 4 | + | [[ebsd2021: |
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| <WRAP center round box 60%> | <WRAP center round box 60%> | ||
| - | Tema 5 | + | [[ebsd2021: |
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| - | Tema 6 | + | [[ebsd2021: |
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| <WRAP center round box 60%> | <WRAP center round box 60%> | ||
| - | Tema 7 | + | [[ebsd2021: |
| </ | </ | ||
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| Discussions, | Discussions, | ||
| ~~DISCUSSION~~ | ~~DISCUSSION~~ | ||
ebsd2021/raissy.1630430702.txt.gz · Last modified: 2021/08/31 14:25 by escola