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Math 457 SPRING 2012, List of lectures
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On this page I will post content of all lectures. All handouts also will be posted here.
Monday, April 2: Examples of dynamical systems. Chapter 2.
Reading assignment: Read Sections 3.1-3.4.
Please find your homework!
Wednesday, April 4: Orbits. Chapter 3. Reading assignment: Read
Sections 3.5-3.6.
Friday, April 6: Doubling function and binary expansions.
Chapter 3. Reading assignment: Read Chapter 4.
Monday, April 9: Graphical analysis. Chapter 4. Reading assignment: Read
Chapter 5.
Wednesday, April 11: The Fixed Point Theorem. The Attractive and Repelling
Fixed Point Theorems. Chapter 5. Reading assignment: Read Chapter 5.
New homework!
Friday, April 13: Proof of the Attractive Fixed Point Theorem.
Chapter 5. Reading assignment: Read Chapter 6.
Monday, April 16: Neutral fixed points.
Quadratic family. Chapters 5 and 6. Reading assignment: Read Chapter 6.
Wednesday, April 18: Fixed points and attracting 2-cycle for
quadratic family.
Section 6.1. Reading assignment:
Read Sections 6.2-6.3. New homework!
Friday, April 20: The Saddle-Node bifurcation and
the Period-Doubling bifurcation.
Sections 6.2-6.3. Reading assignment: Start reading Chapter 7.
Monday, April 23: Quadratic family for c<-2. Chapter 7.
Reading assignment: Read Section 7.3. We will have MIDTERM on Friday!!!
Please find here review sheet.
Wednesday, April 25: The function T_3(x) and the Cantor set.
Chapter 7. Reading assignment: get ready for midterm!
Friday, April 27: MIDTERM.
Monday, April 30: Orbit diagram.
Transition to chaos via period-doubling. Chapter 8.
Wednesday, May 2: Itineraries for quadratic family.
Metric spaces. Chapter 9. Reading assignment: Read Sections 9.2-9.3.
New homework!
Friday, May 4: When dynamics of two functions are the "same"?
Chapter 9. Reading assignment: Read Section 9.4.
Monday, May 7: The conjugacy theorem and its proof. Section 9.4.
Wednesday, May 9: More examples of conjugacy. Chapter 9.
New homework!
Friday, May 11: Chaotic dynamical systems.
Section 10.1.
Monday, May 14: Histograms. Other chaotic systems.
Section 10.2.
Wednesday, May 16: Feigenbaum constant.
Period 3 Theorem and Sarkovskii's Theorem. Sections 10.4, 11.1, 11.2.
New homework!
Friday, May 18: Proof of Period 3 Theorem. Section 11.1
Monday, May 21: The Schwartian Derivative. Section 12.1.
We will have MIDTERM on Friday!!!
Please find here review sheet.
Wednesday, May 23: The critical points and basins of attraction.
Section 12.2. Reading assignment: get ready for midterm!
Friday, May 25: MIDTERM.
Monday, May 28: Memorial Day.
Wednesday, May 30: Complex numbers. Sections 15.1-15.2.
Last homework!
Friday, June 1: Dynamics of complex linear functions.
Calculus of Complex Functions. Sections 15.3-15.4.
Monday, June 4: Calculus of Complex Functions. Section 15.4.
Wednesday, June 6: Julia sets. Chapter 16.
Friday, June 8: The Mandelbrot Set. Chapter 17.
Please find
here review sheet. IMPORTANT: Final is cummulative,
so please look at previous review sheets as well!
THE END.