Mathematics 3DC3:
Discrete Dynamical Systems and Chaos
(Fall, 2010)

Course Information

Course Objectives: The two objectives of the course are to elaborate the elements of analysis of discrete dynamical systems and to consider particular systems with complex (chaotic) behavior. The elements of the discrete dynamical system theory include existence and stability of fixed points and periodic orbits, various bifurcations and global behavior. The elements of chaos include detailed studies of quadratic maps, Cantor sets, symbolic dynamics, conjugacy, fractals, and the Julia and Madelbrot sets. Lectures and exams contain both the results and the derivations. Home assignments include analytical and computational problems.

Topics: Iteration of functions: orbits, graphical analysis, fixed and periodic points, stability, bifurcations, chaos, fractals.

Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail:
Office hours: Mondays and Wednesdays (15:30-16:20), or by appointment

Lectures: Mondays, Wednesdays, and Thursdays (16:30-17:20); ABB/270

"A First Course in Chaotic Dynamical Systems" by R.L. Devaney (Perseus Books Publishing, 1992), ISBN 0-201-55406-2.

Optional Textbooks:
"Discrete Chaos" by S.N. Elaydi, Second Edition (Chapman, Hall/CRC, 2008), ISBN 978-1-58488-592-4.
"Invitation to Dynamical Systems" by E.R. Scheinerman (Prentice Hall, 1996), out-of-print but available electronically.

Lectures: There will be three lectures per week. The lectures will be used to present new material as well as to review the material for assignments and midterms.

Assignments: Six home assignments will be posted on the course webpage every second week. The assignments are to be dropped in the course locker any time before and on the date of the deadline. Only five best results are accounted in the final mark. Solutions to assignments will be posted on the course webpage. You may discuss problems of the assignments with each other, but we expect you to write up the answers by yourself. You may not copy another student's solution.

Class Tests: There will be two class tests, tentatively scheduled on Thursdays October 7 and November 4 during the regular class hour. Only the McMaster standard calculator Casio fx-991 is allowed on the tests. You must bring your student ID to the test room. Solutions to tests will not be posted on the course webpage.

Final Exam: The course is completed by a three-hour final examination. The date and location of the final exam will be announced by the registrar's office before the end of term.

Marking scheme:
Final exam (3 hrs) - 40%
Class tests (50 min - two) - 40%
Homework assignments (best five) - 20%

Senate Policy Statement: The course is regulated under the following documents: Statement on Academic Ethics and Senate Resolutions on Academic Dishonesty. Any student who infringes one of these resolutions will be treated according to the published policy. In particular, academic dishonesty includes (1) plagiarism, e.g. the submission of work that is not one's own, (2) improper collaboration in group work on home assignments, (3) copying or using unauthorized aids tests and examinations. It is your responsibility to understand what constitutes academic dishonesty, refering to Academic Integrity Policy.

Important information: The instructor and university reserve the right to modify elements of the course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.

Additional information: Late assignments will not be marked. No make-up tests will be scheduled. Exemptions from the tests and assignments for valid reasons are possible, but must be requested through the office of the Associate Dean of the Faculty you are registered with. In the event of an exemption, your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or assignment.