Math 117: Dynamical Systems (Winter 2017)

 

Course Code: 45020

    

MWF 11:00 – 11:50 // MSTB 114

Midterm Exam: Friday, February 10, 11:00 - 11:50am

Final Exam: Friday, March 24, 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

Teaching Assistant: Michael Porter
        Office Hours: Tu 3:00-5:00 pm, WTh 9:30-10:30 am

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 Thursday, January 19): problems 3.7, 3.10, 3.16, 3.19, 4.1, 4.4, 5.1.

Homework 2 (due Thursday, January 26).

Homework 3 (due Thursday, February 2).

Homework 4 (due Thursday, February 9): problems 9.12, 9.13, 9.18, 9.19, 10.10, 10.21, 10.27.

Sample Midterm

Homework 5 (due Thursday, February 23).

Homework 6 (due Thursday, March 2).

Presentation on fractals

Homework 7 (due Thursday, March 9).

Homework 8 (due Thursday, March 16): problems 15.2, 15.3, 15.8, 15.11, 16.1, 16.2, 16.4.

Sample Final

 

 

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