Math 117: Dynamical Systems (Winter 2020)

 

Course Code: 45020

    

MWF 11:00 – 11:50 // MSTB 114

Final Exam: Friday, March 20, 8:00-10:00am  

Instructor: Anton Gorodetski
        Email: asgor@uci.edu
        Phone: (949) 824-1381
        Office Location: RH 510G
        Office Hours: MW 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%.

In the theory of dynamical systems we study 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 January 16 in class)

Homework 2 (due January 23 in class)

Homework 3 (due January 30 in class)

Midterm (due February 24 in class)

Homework 4 (due February 6 in class)

Homework 5 (due February 20 in class)

Homework 6 (due  March 5 in class)

Final Exam (due March 13 in class)

 

 

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