Course meeting times: 10:30-11:20 MWF

Course meeting place: 118 MLH

Discussion section meeting time: 10:30-11:20 T

Discussion section meeting place: 218 MLH

Prerequisites: 22M:100 or consent of instructor. A course in differential equations. Some knowledge of computer programming. The languages Matlab and Maple will be used.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday 2:30-4:30 and Wednesday 2:30-3:30. I will also be available at other times. Just drop by my office or send me an e-mail to make an appointment.

Telephone: (319)-335-0898

Fax: (319)-335-0627

E-mail address: ljay@math.uiowa.edu

Mailbox: in Mailroom 15 MLH

Course web page: Assignments and other information about the course will be given in http://www.math.uiowa.edu/~ljay/m142_05.html. Students are responsible for checking regularly this course web page.

Textbook: An Introduction to Dynamical Systems: Discrete and Continuous by R. Clark Robinson, Prentice Hall, 2004, 672 pages, ISBN: 0131431404, list price: $87.00. Table of contents, information and errata on the book by the author. The book on amazon.com. Library reference: ENGINEERING Library QA614.8 .R65 2004.

Additional references:

Stability, instability and chaos by Paul Glendinning, Cambridge University Press, Cambridge texts in applied mathematics, 1994, 388 pages, ISBN: 0-521-42566-2, reprinted 1999.

Dynamical Systems with Applications using Maple, Birkhauser, Boston, 2001, 398 pages, ISBN 0-8176-4150-5, (ENGINEERING Library QA614.8 .L96 2001), and Dynamical Systems with Applications using Matlab Birkhauser, Boston, 2004, 450 pages, ISBN 0-8176-4321-4, (ENGINEERING Library QA614.8 .L97 2004), both books by Stephen Lynch,

Nonlinear dynamics and chaos by Steven H. Strogatz, Westview Press, 1994, ISBN: 0-7382-0453-6, (MATH Q172.5.C45 S767 1994).

An introduction to chaotic dynamical systems, Second edition by Robert L. Devaney, Addison-Wesley, Addison-Wesley Studies in Nonlinearity, 1989, 336 pages, ISBN: 0-201-13046-7, (PHYS QA614.8 .D48 1988, MATH QA614.8 .D48 1986).

Chaos: an introduction to dynamical systems by Kathleen T. Alligood, Tim D. Sauer, James A. Yorke, Springer, New York, Textbooks in mathematical sciences, 1997, 603 pages, ISBN: 0387946772, (MATH QA614.8 .A44 1997).

Goals and objectives of the course: This course is a graduate course and it is assumed that you can work along the course in an independent fashion. This course will cover continuous and discrete dynamical systems (linear/nonlinear differential equations and iterated maps), one- and two-dimensional flows, stability, phase plane, limit cycles, bifurcations, chaos, fractals, numerical methods for dynamical systems, and applications. At the end of the course the student should master essential issues in those topics.

Class procedures: The majority of each class period will be lecture oriented. It is strongly advised to read the material to be discussed before coming to class.

Computer languages: Matlab and Maple.

Computer resources: Computer accounts will be made available on the network in MLH B5. Check the laboratories reservation schedule and the web page of the Division of Mathematics Sciences Educational Laboratories for more information.

Grading procedures: The final grade will be based on one mid-term examination, the final examination, and homework, as follows:

1. The mid-term examination and the final examination will each account for 30% of the course grade.
2. Homework and project assignments will account for 40% of the course grade. Late homework will be accepted only by special permission of the instructor. The grade for your homework will be based on the best 75% of your homework.

The tests are open books and open notes examinations. Bring a scientific calculator. In assigning grades, plus/minus grading will be used.

Teaching assistant: Joaquin Rivera, e-mail: rvera@math.uiowa.edu.

Final examination: To be held on Thursday, December 15, 2005, 9:45-11:45 A.M. in room 210 MLH. Only under exceptional circumstances will a student be permitted to shift the time of this examination. This final examination is an open books and open notes examination. Bring a scientific calculator.

Course outline: see Table of contents. Examples of topics:

• Linear/nonlinear differential equations;
• Trajectories, phase space, flows, limit sets;
• Derivatives with respect to initial conditions, the resolvent;
• Critical points, invariant manifolds;
• Stable, unstable, and center manifolds;
• Periodic orbits, limit cycles, Poincare maps, Floquet theory;
• Hamiltonian systems, Liapunov functions and stability;
• Modelling interacting species;
• Bifurcation theory;
• Local and global bifurcations;
• Three dimensional autonomous systems and chaos, Lyapunov exponents;
• Cascades, the Feigenbaum number;
• Homoclinic orbits, heteroclinic orbits;
• Strange attractors;
• The second part of David Hilbert's 16'th problem;
• Limit cycles of Lienard systems;
• Complex iterative maps;
• Fractals;
• Multifractals;
• Controlling chaos;
• etc.

This course plan may be modified during the semester. Such modifications will be announced in advance during class periods and on the course web page; the student is responsible for keeping abreast of such changes.

Notes to student: The Department of Mathematics has offices in 14 MLH. To make an appointment to speak with the Chair of the Department, call 335-0714 or contact the Departmental Secretary in 14 MLH.

Please let your instructor know if you have a disability that requires special arrangements.

This course is given by the College of Liberal Arts and Sciences. This means that class policies on matters such as requirements, grading, and sanctions for academic dishonesty are governed by the College of Liberal Arts and Sciences. Students wishing to add or drop this course after the official deadline must receive the approval of the Dean of the College of Liberal Arts and Sciences. Details of the University policy of cross enrollments may be found at: http://www.uiowa.edu/~provost/deos/crossenroll.doc.

Cell phones and pagers must be on silent mode during lecture. CELL PHONES AND PAGERS ARE NOT ALLOWED IN CLASS DURING EXAMS. If you do bring a cell phone or pager to an exam, you may leave it in the front of the class during the exam. If a student is found to have a cell phone or pager during an exam, the cell phone or pager will be taken from the student and procedures for cheating may be followed.