Date |
Topics |
Assignments |
Jan 29 & 31
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Class starts: Tuesday Jan 29
1. Introduction
1.1 Review of complex numbers
1.2 Dynamical Systems and the Logistic Family
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|
Feb 5 & 7
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1.3 Background Material and Notation
2. First Steps in Complex Iteration
2.1 & 2.2 Orbits and Iteration
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Homework I
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Feb 12 & 14
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2.3 Iterating the Logistics Maps
2.4 Periodic Points and their Multipliers
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|
Feb 19 & 21
|
30 min. Student Presentations Start
2.5 The Basin of Infinity of a Polynomial
2.6 Iterating Transcendental Functions
2.7 Affine Conjugacy
2.8 Equicontinuity
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Feb 19
2.5 Alexander Pacun
2.6 Moshe Stein
Feb 21
2.7 Jiayong Zhu
2.8 Emi Brawley
Homework II
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Feb 26 & 28
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3. Riemann Sphere
3.1 Stereographic Projection/Chordal Distance
3.2 Spherical Derivative and Meromorphic Functions
3.3 Moebius Transformations I
3.4 Moebius Transformations II
|
Feb 26
3.1 Sachin Seth
3.2 Kunhui Luan
Feb 28
Nicole Sayad
Janine Villarreal
Homework III
|
March 5 & 7
|
4. Fatou and Julia sets
4.1 Definitions of the Fatou and Julia sets I
4.1 Definitions of the Fatou and Julia sets II
The Geometry of Julia Sets I
The Geometry of Julia Sets II
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March 5
4.1-I
4.1-II Jinzheng Li
March 7
Geometry-I Brandon Gontmacher
Geometry-II Moshe Dinowitz
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March 12 & 14
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4.2 The Filled-in Julia set of a Polynomial and Exceptional Set I
4.2 The Filled-in Julia set of a Polynomial and Exceptional Set II
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March 12
4.2-I Hubert Puszklewicz
4.2-II Pete Coletti
March 14
No class
|
March 19 & 21
|
Spring Break !
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|
March 26 & 28
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4.3 The Boundary of the Filled-in Julia Set I
4.3 The Boundary of the Filled-in Julia Set II
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March 26
4.3-I Liuming Wang
4.3-II Connor Stewart
Homework IV
March 28
No class
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April 2 & 4
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5. Components of the Fatou set/Normal Families
5.1 Normal Families and Compact Convergence I
5.1 Normal Families and Compact Convergence II
5.2 Components of the Fatou Set: Constant Limit Functions I
5.2 Components of the Fatou Set: Constant Limit Functions II
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April 2
5.1-I Hanning Wang
5.1-II Yanming Cao
April 4
5.2 I Spencer Jarrad
5.2-II Pablo Mingwang Zhou Wang
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April 9 & 11
|
Second round of presentations start
5.3 Parabolic Points I
5.3 Parabolic Points II
5.4 Non-Constant Limit Functions and the Classification of Fatou Components
6. Further Properties of the Julia sets; The Fundamental Theorem
6.1 Essential Singularities
|
5.3-I Jiayong Zhu
5.3-II Jinzheng Li
5.4 Nicole Sayad
6.1 Pablo Mingwang Zhou Wang
Homework V
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April 16 & 18
|
6.2 The Julia Set of an Entire Function
6.3 Montel's Theorem and Properties of the Julia Set
6.4 Connecting Normal Families and the Entire Functions: Zalcman's Lemma I
6.4 Connecting Normal Families and the Entire Functions: Zalcman's Lemma II
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6.2 Janine Villareal
6.3 Pete Coletti
6.4-I Liuming Wang
6.4-II Connor Stewart
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April 23 & 25
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6.5 Density of Repelling Periodic Points
7. Singular Values and the Mandelbrot Set
7.1 Singular Values I
7.1 Singular Values II
7.2 The Influence of Singular Values
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6.5 Emi Brawley
7.1-I Yanming Cao
7.1-II Hanning Wang
7.2 Sachin Seth
Homework VI
|
April 30 & May 2
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7.3 The Mandelbrot Set
7.4 The Boundary of the Mandelbrot Set
The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics I
The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics II
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7.3 Spencer Jarrad
7.4 Kunhui Luan
Exp-I: Moshe Dinowitz
Exp-II: Brandon Gontmacher
Homework VII
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May 7 & 9
|
The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics III
The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics IV
The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics V
|
Exp-III Alexander Pacun
Exp-IV Moshe Stein
Exp-V Hubert Puszklewicz
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