動態系統
Dynamical Systems
| 節 | 週二 | 週四 |
|---|---|---|
2 09:00–09:50 | 動態系統 SA213（光復） | |
3 10:10–11:00 | 動態系統 SA213（光復） 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
We teach an introductory course in ergodic theory, which is a central topic in dynamical system. It has widespread connection with analysis, fractal geometry, number theory, and probability theory, etc. 1. Recurrence 2. ergodicity 3. mixing 4. the ergodic theorem 5. factors and joins 6. entropy 7. invariant measures
Calculus (better with measure theory/real analysis, but not required)
無備註
Notes will be provided in class
Quiz: 40% Two Midterm Exams: 60% (with 30% each) Extra 10% for reporting
教師未提供此項資料
| 週次 | 主題 |
|---|---|
| 第 1 週 | preliminaries; what is ergodic theory; measure theory foundations 2026-02-24(二),2026-02-26(四) |
| 第 2 週 | examples of ergodic transforms 2026-03-03(二),2026-03-05(四) |
| 第 3 週 | normal number theorem; recurrence 2026-03-10(二),2026-03-12(四) |
| 第 4 週 | ergodicity 2026-03-17(二),2026-03-19(四) |
| 第 5 週 | ergodic decomposition 2026-03-24(二),2026-03-26(四) |
| 第 6 週 | mixing 2026-03-31(二),2026-04-02(四) |
| 第 7 週 | mixing and ergodicity 2026-04-07(二),2026-04-09(四) |
| 第 8 週 | the ergodic theorem 2026-04-14(二),2026-04-16(四) |
| 第 9 週 | the ergodic theorem 2026-04-21(二),2026-04-23(四) |
| 第 10 週 | factors and joins 2026-04-28(二),2026-04-30(四) |
| 第 11 週 | entropy 2026-05-05(二),2026-05-07(四) |
| 第 12 週 | entropy 2026-05-12(二),2026-05-14(四) |
| 第 13 週 | invariant measures 2026-05-19(二),2026-05-21(四) |
| 第 14 週 | invariant measures 2026-05-26(二),2026-05-28(四) |
| 第 15 週 | topological entropy 2026-06-02(二),2026-06-04(四) |
| 第 16 週 | 彈性內容 2026-06-09(二),2026-06-11(四) |
2000 Walters - An Introduction to Ergodic Theory (published by Springer-Verlag) ---- This is the standard textbook, but it is a little too advanced for this course. We will use it as a reference, but we will prepare our own, more elementary lecture notes.
- 地點
- SA 320
- 時間
- By appointment
- 聯絡方式
- xfang@nycu.edu.tw