Course Objectives: The two objectives of the course are to study elements of analysis of discrete dynamical systems and to illustrate dynamics of specific applied systems with complex (chaotic) behavior. The elements of analysis include existence and stability of fixed points and periodic orbits, various bifurcations and global behavior. The specific applied systems include logistic maps, Cantor sets, symbolic dynamics, conjugacy, fractals, and the Julia and Madelbrot sets. The course covers the following topics: iteration of functions, orbits, graphical analysis, fixed and periodic points, stability, bifurcations, chaos, fractals.
Instructor:
Dr. Dmitry Pelinovsky, HH-422, ext.23424,
e-mail: dmpeli@math.mcmaster.ca
Hours:
Lectures: Tuesdays, Thursdays, and Fridays (11:30-12:20); HH/305
Office hours: Tuesdays and Fridays (10:30-11:20), or by appointment.
Textbook:
"A First Course in Chaotic Dynamical Systems: Theory and Experiment"
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.
"Differential Equations, Dynamical Systems, and an Introduction to Chaos"
by M.W. Hirsch, S. Smale, and R.L. Devaney (Academic Press, 2013), third edition,
ISBN 978-0-12-382010-5.
Assignments: Five 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 four best results are accounted in the final mark. 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 scheduled on January 29 and March 20 during the regular class hour. The McMaster standard calculator Casio fx-991, the textbook, and the class notes are allowed on the tests. You must bring your student ID to the test room.
Final Exam: The course is completed by a two-hour final examination. The examination will take place on April 7 in HH-305 for 11:30-1:30.
Marking scheme:
Final exam (2 hrs) - 40%
Class tests (50 min - two) - 40%
Homework assignments (best four) - 20%
Important message: 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.
Academic Dishonesty: Any student
who infringes academic dishonesty will be treated according
to the policy of the McMaster University. 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.
Requests for Relief for Missed Academic Term Work: Using the McMaster student absence form (MSAF) on-line, self-reporting tool, undergraduate students may report absences lasting up to 5 days and may also request relief for missed academic work, which is less than 30% of the final mark. The submission of medical or other types of supporting documentation is normally not required. Students may use this tool only once per term. Students who are absent more than five days cannot use the on-line, self-reporting tool to request relief. They MUST report to their Faculty Office to discuss their situation and may be required to provide appropriate supporting documentation.
Additional information: Late assignments will not be graded. No make-up tests will be scheduled. In the event of an exemption from the test or more than one assignment, your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or assignment.