This calendar is extremely tentative, but should give a general idea of what topics we will cover.
Course Textbooks:
| Date | Tentative class plan: |
| Thu, Aug 25 | Introduction to dynamical systems (roughly following Devaney's I.1-I.2). Introduction to topological conjugacy. (Not introduced in the book until Devaney I.7). |
| Tue, Aug 30 | Examples of Dynamical Systems (perhaps different than Devaney I.2). Devaney A.1: Preliminaries from Calculus. Devaney A.2: Preliminaries from Geometry and Topology. Devaney I.3: Elementary Definitions. A note clarifying definitions of forward asymptotic. |
| Thu, Sep 1 | Devaney I.4: Hyperbolicity. |
| Tue, Sep 6 | Conjugacy in homeomorphisms. Start Devaney I.5: The Logistic Family of Maps. |
| Thu, Sep 8 | Continue Devaney I.5: The Logistic Family of Maps. Discuss Cantor Sets. |
| Tue, Sep 13 | Devaney I.5: The Logistic Family of Maps. |
| Thu, Sep 15 | Class held in NAC 1/511. Finish Devaney I.5: The Logistic Family of Maps. Experimenting with dynamics of functions using Sage. |
| Tue, Sep 20 | Class held in NAC 1/511. Review for the midterm. |
| Thu, Sep 22 | Midterm 1. |
| Tue, Sep 27 | No classes scheduled |
| Thu, Sep 29 | No class (Classes follow a Monday schedule) |
| Tue, Oct 4 | No class scheduled |
| Thu, Oct 6 | Devaney I.6: Symbolic Dynamics. |
| Tue, Oct 11 | Devaney I.7: Topological Conjugacy. |
| Thu, Oct 13 | Semiconjugacy (from the end of section I.7). |
| Tue, Oct 18 | Devaney I.9: Structural Stability. |
| Thu, Oct 20 | Devaney I.8: Chaos. |
| Tue, Oct 25 | Devaney I.10: Sharkovsky’s Theorem. |
| Thu, Oct 27 | Devaney I.10: Sharkovsky’s Theorem. Devaney I.10: Sharkovsky’s Theorem. |
| Tue, Nov 1 | Devaney I.11: The Schwarzian Derivative. |
| Thu, Nov 3 | Midterm 2. |
| Tue, Nov 8 | Finish Devaney I.11: The Schwarzian Derivative. |
| Thu, Nov 10 | Devaney I.12: Bifurcations. |
| Tue, Nov 15 | Devaney III.28: The Smale Horseshoe Map. Please read Devaney III.27: Dynamics of Linear Maps. |
| Thu, Nov 17 | Devaney I.16: Maps of the Circle. |
| Tue, Nov 22 | Devaney III.29: Hyperbolic Toral Automorphisms. Lecture posted on blackboard due to illness.. |
| Thu, Nov 24 | College closed (Happy Thanksgiving!) |
| Tue, Nov 29 | Continue Devaney I.16: Maps of the Circle. Begin discussing Poincaré's Theorem for circle homeomorphisms. |
| Thu, Dec 1 | Finish Devaney I.16: Maps of the Circle. |
| Tue, Dec 6 | Devaney III.30: Attractors. |
| Thu, Dec 8 | Finish Devaney III.30: Attractors. Discuss Markov Partitions in the context of toral automorphisms and the solenoid.. |
| Tue, Dec 13 | Midterm 3. |
The Final Presentation will be held when the final exam is scheduled by the college: Tuesday, December 20th from 6pm to 8:15pm.