Math 457 SPRING 2012, List of lectures

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.