Math 407      Chaos and Fractals
Instructor	Office	Phone	Hours
Jimmie Lee Johnson	Auditorium Campus, Room 416	(312) 341-3552 Voice Mail	by appointment
E-mail:  jjohnson@roosevelt.edu Web Page: http://faculty.roosevelt.edu/jjohnson/Fall2003/M407F03.htm

Text: Chaotic Dynamical Systems , by Robert Devaney, Westview Press, 2nd ed. 2003.

Prerequisite: Grades of C or better in Math 233, Calculus III and Math 300, Linear Algebra. Math 307, Differential Equations and Modeling is recommended, but not required.

Homework will be discussed, collected, graded and returned; please leave the assignment on the instructor's desk whether I ask for it or not. Some of the homework will require the use of technology such as graphing calculators, Maple, and the software bundled with the text. Homework will count for 30% of your grade. Late homework will be accepted, but at a reduced value as the lateness increases. Homework later than one week after the appropriate exam will not be graded. Homework later than the last regular class day will not be graded. This does not apply to the last homework assignment which will be accepted, perhaps with reduced credit, at the time of the final exam.

Exams will be given on Thursdays, October 2nd and November 6th or as otherwise arranged in advance. Each will be closed book, and may require the use of technology, and their average will each count for 35% of your grade. No make-ups except for excused absences with advance notice. The score on the next test will be used for both.

Final Examination: It will be given on Thursday, December 18th, comprehensive and closed book with a portion requiring the use of technology; it will count for 35% of your grade.

Grades: Regulations covering grades (especially I and W) are on pages 265-267 of the 2002-2004 Undergraduate Catalog or on pages 188-190 of the 2001-2003 Graduate Catalog. Incompletes will not be given, except to a student who has done passing work up to the Final Examination (including most of the homework) but misses the final exam because of an excused absence with advance notice. The last day to drop a class (with a grade of "W") is Friday, November 14, and the drop form must be submitted to the Registrar's Office. Anyone registered after that must be graded solely on academic performance.

Syllabus ( The main objective is to learn to examine iterated functions and any chaotic behavior. )

Date Sections        Topics September 4 1.1, 1.2, 1.3 Examples, Preliminaries, Definitions September 11 1.4, 1.5, 1.6 Hyperbolicity, Quadratic Family, Symbolic Dynamics September 18 1.7, 1.8, 1.9 Topological conjugacy, Chaos, Stability September 25 1.10,1.11,1.12 Sarkovskii, Schwarzian, Bifurcations October 2 Exam #1 Sections 1.1-1.9 October 9 1.13,1.14, Period Three, Maps of the Circle October 16 1.15,1.16 Diffeomorphisms, Homoclinic points October 23 1.17,1.18 Period Doubling, Kneading October 30 1.19, 2.1 Geneology, More Preliminaries November 6 Exam #2 Sections 1.10-1.18 November 13 2.2, 2.3 Linear Maps, Horseshoe Map November 20 2.4, 2.5 Hyperbolic Toral Automorphisms, Attractors December 4 2.6, 2.7 Stable-Unstable Manifold Theorem, Global Results. December 11 2.8,2.9 Hopf Bifurcation, Henon Map December 18 Final Exam Comprehensive.

This page is at http://faculty.roosevelt.edu/jjohnson/Spring2003/M407F03.htm and was last revised July 23, 2003