| Lec. | Date | Topic |
|---|---|---|
| 1 | 8/25 | Dynamics in nature: populations. |
| 2 | 8/27 | Dynamics in mathematics and games. |
| 3 | 8/29 | First digits of powers and circle rotations. |
| 9/1 | - Labor Day - | |
| 4 | 9/3 | Equidistribution on the circle. Discrete-time dynamical systems. |
| 5 | 9/5 | Fixed and periodic points. Basic examples. |
| 6 | 9/8 | Contractions in one dimension. |
| 7 | 9/10 | The Contraction Mapping Principle. |
| 8 | 9/12 | An application
to Fibonacci numbers. Attracting fixed points. |
| 9 | 9/15 | Non-decreasing maps of an interval. |
| 10 | 9/17 | Autonomous differential equations. |
| 11 | 9/19 | Existence and uniqueness of solutions. |
| 12 | 9/22 | Linear maps in the plane. |
| 13 | 9/24 | Linear maps in the plane. |
| 14 | 9/26 | Topological conjugacy. Linear differential equations. |
| 15 | 9/29 | Linear differential equations. Flows. |
| 16 | 10/1 | Fractals. |
| 17 | 10/3 | Fractals in complex dynamics. |
| 10/6 | Midterm exam: 497A, 10:10 a.m. - 12:05 p.m. | |
| 10/7 | Midterm exam: 497C, 10:10 a.m. - 12:05 p.m. | |
| 10/8 | Midterm exam: 497B, 10:10 a.m. - 12:05 p.m. | |
| 18 | 10/10 | Homeomorphisms. |
| 19 | 10/13 | Recurrence. |
| 20 | 10/15 | Recurrence. |
| 21 | 10/17 | Transitivity and minimality. |
| 22 | 10/20 | The times-m map of the circle. |
| 23 | 10/22 |
The times-m map of the circle. Sequence spaces. |
| 24 | 10/24 | Symbolic dynamical systems. |
| 25 | 10/27 | Expanding maps of the circle. |
| 26 | 10/29 | Coding. |
| 27 | 10/31 | Toral automorphisms. |
| 28 | 11/3 | Hyperbolic toral automorphisms. |
| 29 | 11/5 | Periodic points of hyperbolic toral automorphisms. |
| 30 | 11/7 | Coding for a hyperbolic toral automorphism. |
| 31 | 11/10 | Topological entropy: definition and examples. |
| 32 | 11/12 | Topological entropy: properties. |
| 33 | 11/14 | More on topological entropy. |
| 34 | 11/17 | Topological mixing. |
| 35 | 11/19 | Criteria for topological transitivity. |
| 36 | 11/21 | Chaos. Sensitive dependence on initial conditions. |
| 37 | 12/1 | Sensitive dependence, topological mixing, and chaos. |
| 38 | 12/3 | Topological entropy revisited. |
| 39 | 12/5 | Topological mixing, transitivity, and minimality revisited. |