| Lec. | Date | Topics | Chapter |
|---|---|---|---|
| 1 | 1/7 | Dynamics in nature. | 1 |
| 2 | 1/10 | Dynamics in mathematics. Linear maps of R. | 1, 2 |
| 3 | 1/14 | Orbits, fixed and periodic points. Examples. Graphs. | 2 |
| 4 | 1/17 | Contractions in Euclidean space. | 2 |
| - | 1/21 | -- MLK Day -- | |
| 5 | 1/23 | Applications of the Contraction Principle. Attracting fixed points. |
2 |
| 6 | 1/28 | Superattracting fixed points. Nondecreasing interval maps. Differential equations on the line. |
2 |
| 7 | 1/30 | Cantor set. Fractals. | 2 |
| 8 | 2/4 | Mandelbrot set and Julia sets. | |
| 9 | 2/6 | Dimension: fractal, box-counting, Hausdorff. | |
| 10 | 2/11 | Circle rotations. Density of orbits. | 4 |
| 11 | 2/13 | Recurrence. Transitive and minimal homeomorphisms. | 4 |
| 12 | 2/18 | Circle rotations: Equidistribution. | 4 |
| 13 | 2/20 | First digits of powers, last digits of powers and of n2. | 1, 4 |
| 14 | 2/25 | Linear flow on the 2-torus. | 4 |
| 15 | 2/27 | Billiards. | 4 |
| 16 | 3/3 | Eigenvalues and eigenvectors - review. Linear maps or R2 with two distinct real eigenvalues. |
3 |
| 17 | 3/5 | Maps with one real or two complex conjugate eigenvalues. | 3 |
| - | 3/10-16 | -- Spring break -- | |
| 18 | 3/17 | Midterm Exam | |
| 19 | 3/19 | Linear maps of R2 -- long-term behavior. | 3 |
| 20 | 3/24 | Linear maps of R2 -- long-term behavior. | 3 |
| 21 | 3/26 | Linear maps of the 2-torus. | |
| 22 | 3/31 | Hyperbolic linear maps of the 2-torus -- eigenvalues, eigen-directions, periodic points. |
7 |
| 23 | 4/2 | A criterion for topological transitivity. | 7 |
| 24 | 4/7 | Mixing. Arnold's cat map. | 7 |
| 25 | 4/9 | Chaos. | 7 |
| 26 | 4/14 | Coding. Example. | 7 |
| 27 | 4/16 | Implications of coding. | 7 |
| 28 | 4/21 | Topological entropy. | 8 |
| 29 | 4/23 | Review. |