Math 117: Dynamical Systems (Winter 2015)

 

Course Code: 45020

    

MWF 11:00 – 11:50 // PSCB 240

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:  A first course in chaotic dynamical systems, by Robert Devaney.

Preliminary syllabus.

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

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 Friday, January 15).

Homework 2 (due Monday, January 26): Chapter 4, problem 1 (a.-d.); Chapter 5, problems 1 (a.-f.), 2 (a.-c.), 3; Chapter 6, problem 15.

Homework 3 (due Monday, February 2): Chapter 7, problems 10, 11; Chapter 9, problems 10, 13, 15.

Homework 4 (due Monday, February 9): Chapter 11, problems 2, 3, 9, 15, 16.

Sample Midterm

Homework 5 (due Monday, February 23).

Homework 6 (due Wednesday, March 4): Chapter 12, problems 1, 2, 5, 7, 8.

Homework 7 (due Wednesday, March 11).

Sample Final

 

 

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