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Math 457 SPRING 2011, 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, March 28: Examples of dynamical systems. Chapter 2.
Please find your homework!
Wednesday, March 30: Orbits. Chapter 3. Reading assignment: Read Chapter 4.
Friday, April 1: More on orbits. Doubling function and binary expansions.
Chapter 3. Reading assignment: Read Chapter 4.
New homework!
Monday, April 4: Graphical analysis. Chapter 4. Reading assignment: Read
Chapter 5.
Wednesday, April 6: The Fixed Point Theorem. The Attractive and Repelling
Fixed Point Theorems. Chapter 5. Reading assignment: Read Chapter 5.
Friday, April 8: Proof of the Attractive Fixed Point Theorem.
Chapter 5. Reading assignment: Read Chapter 6.
New homework!
Monday, April 11: Attractive and repelling cycles. Neutral fixed points.
Quadratic family. Chapters 5 and 6. Reading assignment: Read Chapter 6.
Wednesday, April 13: Attractive 2-cycle for quadratic family.
The Saddle-Node Bifurcation. Chapter 6.1-6.2. Reading assignment:
Read Chapter 6.3.
Friday, April 15: The Period-Doubling bifurcation.
Chapter 6.3. Reading assignment: Start reading Chapter 7.
New homework!
Monday, April 18: Quadratic family for c<-2. Cantor sets. Chapter 7.
Reading assignment: Read Section 8.1. We will have MIDTERM on Friday!!!
Please find here review sheet.
Wednesday, April 20: Transition to chaos through period-doubling.
Chapter 8. Reading assignment: get ready for midterm!
Friday, April 22: MIDTERM. Please find here
solutions. New homework!
Monday, April 25: Transition to chaos via period-doubling. When 3-cycle
shows up in the quadratic family. Chapter 8.
Wednesday, April 27: Lecture was cancelled. Homework is extended till
Monday.
Friday, April 29: When dynamics of two functions are the "same"?
Chapter 9. Reading assignment: try to read Chapter 9.
Monday, May 2: Metric spaces. The sequence space and the shift map.
Sections 9.2-9.3. New homework!
Wednesday, May 4: Shift map is continuos. The conjugacy theorem.
Section 9.4.
Friday, May 6: More examples of conjugacy. Chapter 9.
Monday, May 9: Chaotic dynamical systems.
Section 10.1. New homework!
Wednesday, May 11: Other chaotic systems.
Section 10.2.
Friday, May 13: Feigenbaum constant.
Period 3 Theorem and Sarkovskii's Theorem. Sections 10.4, 11.1, 11.2.
Monday, May 16: Proof of Period 3 Theorem. Orbit of the critical poit.
Sections 11.1, 12.2. We will have MIDTERM on Friday!!!
Please find here review sheet.
New homework!
Wednesday, May 18: The Schwartian Derivative. Sections 12.1-12.2.
Reading assignment: get ready for midterm!
Friday, May 20: MIDTERM. Please find here
solutions.
Monday, May 23: Complex numbers. Dynamics of complex linear functions.
Sections 15.1-15.3. New homework!
Wednesday, May 25: Calculus of Complex Functions. Section 15.4.
Friday, May 27: Julia sets. Chapter 16.
Wednesday, June 1: The Mandelbrot Set. Chapter 17.
Friday, June 3: Review. Please find
here review sheet. IMPORTANT: Final is cummulative,
so please look at previous review sheets as well! There will be additional
office hours on Monday, 10-11am.
THE END.