Math 457 SPRING 2011, List of lectures

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.