MA 771: Introduction to Dynamical Systems, Spring 2025
Logistical Information
Location: 685-725 Comm Ave CAS 323A
Time: Tuesday and Thursday, 11AM - 12:15PM
Instructor Information
Lecturer: Malavika Mukundan
Office Hours: Monday 11AM-1PM, Tuesday 2PM-3PM
Email: mmukunda@bu.edu
Office: CDS 303
Course Information
This course is meant to provide a foundation in the theory of dynamical systems, focussing on discrete dynamics. The topics we will explore include topological dynamics, low-dimensional mappings, hyperbolic dynamics, and ergodic theory.
Lecture Notes
Please find lecture notes here. These will be updated every week.
Textbook
The main text for this course is Hasselblatt B, Katok A. A First Course in Dynamics: With a Panorama of Recent Developments. Cambridge University Press; 2003. An e-copy is available online here.
We will also be using the following texts as additional references whenever we discuss any measure theoretical argument:
1. Robert Devaney. An introduction to chaotic dynamical systems, 2nd ed.
2. Michael Brin and Garrett Stuck. Introduction to dynamical systems
3. Pierre Collet and Jean-Pierre Eckmann. Concepts and results in chaotic dynamics: A Short Course
4. Clark Robinson. An introduction to dynamical systems : continuous and discrete, 2nd ed.
Grading
Homework will count for 80% of your course grade. There will be a homework set every other week.
At the end of the semester, each student will give a presentation on a topic of their choice that is related to dynamical systems. This presentation will account for 20% of the course grade. Given below is a list of sample topics, but feel free to pick your own!
1. Classification of orientation-preserving circle homeomorphisms
2. Conjugacy between expanding and linear expanding maps of the circle
3. Newtonian Systems
4. Billiards
5. The Lorenz attractor
6. The Hopf bifurcation
7. The Hénon map
Homework
1. Homework 1, due by 5pm on Feb 6
2. Homework 2, due by 5pm on Feb 24
3. Homework 3, due by 5pm on Mar 13
4. Homework 4, due by 5pm on Mar 27