Introduction to Chaotic Dynamical Systems

(Page Under Construction!!)
Tuesday - Thursday: 5:00PM - 6:15PM
Lippitt Hall Room 204

Instructor    Araceli Bonifant  
Office: Lippitt Hall 200 B
Phone: 874-4394

Office Hours:

Book: There is not textbook for this class.

Course Description. Chaotic phenomena flourish in nature. They often originate in systems whose components are governed by simple laws, but whose overall behavior is very complex. The objective of this course is to give an introduction to the theory of chaotic systems.

Prerequisites:MTH 243 or permission of instructor.

Tentative List of Topics:

  • Elementary definitions.

  • Hyperbolicity.

  • The Logistic map.

  • Symbolic dynamics.

  • Topological conjugacy.

  • Chaos.

  • Structural stability.

  • Bifurcation Theory.

  • Sarkovskii's Theorem.

  • Maps of the circle.

  • Homoclinic points and bifurcations.

  • Period doubling route to chaos.

  • The kneading theory.

  • Evaluation Policy:

  • Homework sets:         60%
  • Project I:                     40%
  • Suggested Reading:

  • Dynamical Systems:Stability, Symbolic Dynamics and Chaos, by Clark Robinson.
  • An Introduction to Chaotic Dynamical Systems by Robert Devaney.
  • Any book on Dynamical Systems on R.

    You are expected to abide by the University's civility policy:

    ``The University of Rhode Island is committed to developing and actively protecting a class environment in which respect must be shown to everyone in order to facilitate the expression, testing, understanding, and creation of a variety of ideas and opinions. Rude, sarcastic, obscene or disrespectful speech and disruptive behavior have a negative impact on everyone's learning and are considered unacceptable. The course instructor will have disruptive persons removed from the class.''

    Cell phones, IPods, beepers and any electronic device must be turned off in class!!

    All submitted work must be your own. If you consult other sources (class readings, articles or books from the library, articles available through internet databases, or websites) these MUST be properly documented, or you will be charged with plagiarism and will receive an F for the paper. In some cases, this may result in a failure of the course as well. In addition, the charge of academic dishonesty will go on your record in the Office of Student Life. If you have any doubt about what constitutes plagiarism, visit the following website:, the URI Student Handbook, and UNIVERSITY MANUAL sections on Plagiarism and Cheating at cheating. Any good writer's handbook as well as reputable online resources will offer help on matters of plagiarism and instruct you on how to acknowledge source material. If you need more help understanding when to cite something or how to indicate your references, PLEASE ASK.

    Illness Due to Flu: The H1N1 Flu Pandemic may impact classes this semester. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify me at 874-4394 or email me at of your status, and we will communicate by email or by phone. We will work together to ensure that course instruction and work is completed for the semester.

    The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness. These include: covering your mouth and nose with a tissue when coughing or sneezing; frequently washing your hands to protect from germs; avoiding touching your eyes, nose and mouth; and staying home when you are sick. For more information, please view

    URI information on the H1N1 will be posted on the URI website at, with links to the site.

    Special Accommodations: ``Section 504 of the Rehabilitation act of 1973 and the Americans with Disabilities Act of 1990 require the University of Rhode Island to provide academic adjustments or the accommodations for students with documented disabilities. The student with a disability shall be responsible for self-identification to the Disability Services for Students in the Office of Student Life, providing appropriate documentation of disability, requesting accommodation in a timely manner, and follow-through regarding accommodations requested.'' It is the student's responsibility to make arrangements for any special needs and the instructor's responsibility to accommodate them with the assistance of the Office of Disability Services for Students.