Math 2720, Intro to Dynamical Systems
This course will be an intro to major themes in dynamics: hyperbolicity, ergodicity and symbolic dynamics.
We'll study properties of many classical examples, from linear maps on tori, to geodesic flow on negatively curved manifolds.
Important info
- Read the syllabus above!
- K.M. office hour: Thursday 4-5 (after class), also Wed. 1:45-2:45
- J.K. office hour: Tuesday 11-12 and Thursday 1:30-2:30.
- Lectures: Tu/Th 2:30 - 3:50 pm in Kassar 105.
- We will primarily use the textbook: Introduction to dynamical systems, by Brin and Stuck. This is required, but available freely online from the Brown library.
Other (online) resources are listed on the syllabus.
If you are taking the course for qual credit, you are required to complete homework assignments.
We will have one assignment for each chapter of the book, these will be announced here when
the chapter is finished, along with deadlines.
We'll also post the exercises given in classes.
- Exercises from Jan. 24
For practice, not to hand in.
Optional reading: What are Lyapunov exponents and why are they interesting?
Expository article by Amie Wilkinson, we'll see many of the topics here come up later.
- Homework due Feb. 14 (problem numbers are from Brin and Stuck:)
1.3.5
1.7.1 and 1.7.4
1.9.2, then conclude that the conjugacy discussed in class (between the solenoid and the doubling map inverse limit) is indeed a conjugacy
1.12.3.
- From Feb 5: Taffy pulling machine (video) and
Thiffault's article
- Homework due Thurs, Feb. 28.
2.1.6, 2.2.6, 2.5.7, 2.6.2, and
Show that if f is a homeomorphism of the circle, then the topological entropy of f is 0.
Also: just in case you thought topological entropy made perfect sense... Take a look at Counterexamples in topological entropy by L.W. Goodwin.
- Week of Feb. 26
For reference: Notes related to Thursday's lecture on the Parry meausure, an application of Ruelle-Perron-Frobenius.
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Homework due Thurs, March 21.
3.3.1, 3.3.2, 4.3.5, 4.3.6, and start thinking about a topic for your final presentation
Guidelines for the final presentation:
You may work alone or in a group of 2 or 3 (depending on your topic); but each person should plan to speak for 25 minutes during your presentation
The topic may be anything dynamical systems related: something we touched on or skipped over or won't get to in the book, or something of your own proposing
You should turn in a written proposal (a few paragraphs is fine) on Tues., april 2nd, including the topic, some readings/resources, and your group members.
If you find that you're stuck and need guidance on topics, we'll be available after class both days next week.
The presentations will occur in class during the weeks of April 23 and 30.
- Additional optional readings on hyperbolic dynamics
History of Poincare's discovery of homoclinic tangles
Ergodicity of the geodesic flow on a negatively curved manifolds