Syllabus for MA 771 Introduction to Dynamical Systems

Syllabus for MA 771 Introduction to Dynamical Systems, Fall 2020

Course Information

Lecturer: Ryan Goh

Email: rgoh@bu.edu
Office: MCS 243
Office Hours: Wednesday 1-3pm, Thursday 11am-12pm and by appointment, zoom links for office hours will be posted on the Blackboard course page
Web page: http://math.bu.edu/people/rgoh/

Lectures:

Time: Monday,Wednesday,Friday, 10:10am-11:00 am;
Location: BRB 121
Textbook: "Dynamical Systems, An Introduction" by Luis Barreira, and Claudia Valls; ISBN: 978-1-4471-4834-0. An electronic copy can be accessed and downloaded through the BU library webpage HERE

Additional References
Here are some other references which may provide an alternative viewpoint and presentation of the course material and which you might find useful. I am in the process of putting the texts with a * on reserve at the BU library (note some may also be available via the Hathi-Trust . I will update when I have more information.
  • * "An introduction to chaotic dynamical systems" by Robert Devaney; 2nd ed..
  • * "Introduction to the modern theory of dynamical systems" by Anatoly Katok, and Boris Hasselblatt
  • "Introduction to dynamical systems" by Michael Brin and Garrett Stuck
  • * "Concepts and results in chaotic dynamics: A Short Course" by Pierre Collet and Jean-Pierre Eckmann
  • * "An introduction to dynamical systems : continuous and discrete", by Clark Robinson, 2nd ed..

    Course Webpage: math.bu.edu/people/rgoh/teaching/ma771-fs20/course-page.html

    Course Description:

    Our course will be divided into 4 parts, with a rough timeline (subject to class preference). While we'll generally follow the book, I will intersperse additional examples, topics, and proofs throughout the course (and will provide any reference material if needed.) Also, instead of doing symbolic dynamics as a separate chapter (Ch. 7), I will illustrate their connections and usefulness to the other areas we'll study.
    1. (Weeks 1 - 3) Introductory concepts, examples, and topological dynamics (transitivity, mixing, entropy, conjugacy)
    2. (Weeks 4 - 6) Low-dimensional dynamics (such as circle mappings, interval maps, toral automorphisms)
    3. (Week 7-10) Hyperbolic dynamics (horshoes, invariant cones and manifolds, homoclinic tangles and tangencies, )
    4. (Week 11-14) Ergodic Theory (invariant measures, Birkhoff ergodic theorem, entropy)

    Homework

    Homework and associated readings will be posted on the course webpage. They will be assigned every few weeks and will be due one week after. You are welcome and encouraged to work together on these, but make sure to write them up on your own. Here is the BU CAS Code of Conduct.

    Class presentation

    Each registered student will be required to give a 30-minute presentation on a dynamics related topic of their choosing. This could be a subject in the text, or one of the additional references which we won't get around to covering, or another topic related to your intrests. Some potential topics you could consider are listed below. Presentations will be made near the end of the semester (date and time TBD). You must meet with me at least once by October 16th to discuss your project and its suitability (though you are more than welcome to meet with me more!) and must let me know by October 23rd what you plan to speak about. If you would like, this presentation could also be in the BU dynamics seminar. Please speak to me if you're interested in this.
    Some potential topics (in no particular order):
  • Smooth invariant measures and SRB measures
  • Transversality, genericity, and the Kupka-Smale theorem
  • Normally Hyperbolic Invariant Manifolds
  • Arithmetic Dynamics
  • Complex Dynamics
  • Random dynamical systems
  • Smooth Linearization of maps and normal forms
  • Billiard problems
  • The illumination problem
  • A study and exploration of one of the classic examples of dynamical systems theory such as:
  • Henon map
  • Tent map (could study the Milnor/Thurston theorem)
  • Logistic map
  • The solenoid
  • Feel free to suggest another!

    • Grades

    Your course grade will assigned as follows
  • Homework scores (80% - lowest score dropped)
  • Class Presentation (20%)

    • Learn From Anywhere and Classroom policies

  • Zoom links for lectures and office hours can be found in the course page on Blackboard .
  • All class sessions will be recorded for the benefit of registered students who are unable to attend live sessions (either in person or remotely) due to time zone differences, illness or other special circumstances. Recorded sessions will be made available to registered students ONLY via their password-protected Blackboard account. Students may not share such sessions with anyone not registered in the course and may certainly not repost them in a public platform. Students have the right to opt-out of being part of the class recording. Please contact me to discuss options for attending the course in such cases.
  • I will also post my lecture notes to the blackboard website a day or two after each class.
  • Please let me know ASAP if a you run into issues with connecting to course materials or resources. I will try to make office hours accessible to students in all time zones. Please contact me if you are unable to make any of the sessions and I will try to work something out with you.
  • You are welcome to switch your class participation modality between remote and in-person for any reason. Please let me know if you decide to do so. At the current class size, we do not need to do rotations, and all registered students are able to attend in person each day if desired.
  • We will observe all University mandated COVID-19 policies on social distancing and mask wearing.

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    The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Boston University.