Math 117: Dynamical Systems (Winter 2014)

 

Course Code: 45020

    

MWF 11:00 – 11:50 // PSCB 240

Final Exam: Friday, March 21, 8:00-10:0am  

Instructor: Anton Gorodetski
        Email: asgor@uci.edu
        Phone: (949) 824-1381
        Office Location: RH 510G
        Office Hours: MWF 12:00-1:00pm or by appointment

Textbook: L.Barreira, C.Valls, Dynamical Systems: An Introduction, Springer, 2012.

We will cover Chapters 1-5 and 7. Short introduction to Ergodic Theory (Chapter 8) and Complex Dynamics will also be given, but mostly for general mathematical culture purposes; these topics will not be covered by the homework or the final exam.

Additional Texts:

  • A.Katok, B.Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, any edition.
  • M.Brin, G.Stuck,  Introduction to Dynamical Systems, Cambridge University Press, 2002.

Additional references will be given for a few topics not covered by these books.

Grading: Weekly homework 30%, midetrm 20%, final 50%.

Dynamical systems is the study of the long-term behavior of evolving systems. The modern theory of dynamical systems originated at the end of the 19th century with fundamental question concerning the stability and evolution of the solar system. Attempts to answer those questions led to the development of a rich and powerful field with applications to physics, biology, meteorology, astronomy, economics, and other areas. The mathematical core of the theory is the study of the global orbit structure of maps and flows with emphasis on properties invariant under coordinate changes.

Homework:

Homework #1 (due Friday, January 17): problems 2.1, 2.2, 2.6, 2.11, 2.16.

Homework #2 (due Friday, January 31): problems 3.1, 3.2, 3.4, 3.8, 3.10.

Sample Midterm

Homework #3 (due Monday, February 24).

Homework #4 (due Wednesday, March 5).

Homework #5 (due Wednesday, March 12): problems 6.3, 7.2, 7.8, 7.10, 7.15.

Sample Final

 

 

 

Links