MTH455 
Introduction to Chaotic Dynamical Systems

(Page Under Construction!!)
 
Tuesday - Thursday: 3:30PM - 4:45 PM
Lippitt Hall Room 201

Instructor    Araceli Bonifant  
Office: Lippitt Hall 200 B
Phone: 874-4394
Email: bonifant@math.uri.edu

Office Hours:

Book: There is not book 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 elementary introduction to the theory of chaotic systems.

Prerequisites:MTH 243 or permission of instructor.


Tentative List of Topics:

  • The Tent Map.

  • Lyapunov Exponent.

  • The Logistic Map.

  • Period Doubling.

  • Chaos.

  • Bifurcation Theory

  • Sarkovskii's Theorem

    • Evaluation Policy:

  • Homework sets:         30%
  • Project I:                   35%
  • Project II:                  35%

    • Suggested Reading:

  • Chaos, Fractals and Dynamics: Computer Experiments in Mathematics by Robert Devaney.
  • Chaotic Dynamics and Nonlinear systems by S. Neil Rasband
  • An Introduction to Chaotic Dynamical Systems by Robert Devaney

    • Policy:
    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!!

    You are required to do your own work unless specifically told otherwise by your instructor. In support of honest students, those discovered cheating on assignments or exams will receive a grade of zero on the assignment or exam. Use of unauthorized aids such as cheat sheets or information stored in calculator memories, will be considered cheating. The Mathematics Department and the University strongly promote academic integrity.

    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 bonifant@math.uri.edu 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
    http://www.cdc.gov/flu/protect/habits.htm

    URI information on the H1N1 will be posted on the URI website at
    http://www.uri.edu/news/h1n1, with links to the
    http://www.cdc.gov site.

    Special Accommodations: Students who need special accommodations and who have documentation from Disability Services should make arrangements with their instructor as soon as possible. Students should contact Disability Services for Students, Office of Student Life, 330 Memorial Union, 874-2098.