Lecture by Prof. Takashi Ikegami

1. chaos

2. 1. How to analyze aperiodic time series?
1. stochastic equation
2. Fourier analysis
3. the 3rd method
2. Strange Attractor
3. Forced Duffing’s Oscillator
4. Baker’s transformation
5. Homoclinic tangle
6. Coin toss is embedded
Content

3. Edward Lorentz

5. Lorentz Attractor

6. ρ=28, σ = 10 and β = 8/3
Lorentz equation

7. Driven Duffing’s Oscillator

9. HTTTTHTHTHHTHTHHHHHH,,,,,,,

10. Smale’s horseshoe

11. Baker’s transformation

12. Homoclinic tangle

13. {σn} → {σn+1}
{xn} → {xn+1}
B
f
φ φ

14. 1. Chaotic Evolution and Strange Attractors by David Ruelle: a thin well reviewed introductory booklet.
2. Dynamics: The Geometry of Behavior (Studies in Nonlinearity) by Abraham and Show. This is the
best picture book for the introduction of nonlinear dynamics and chaos.
3. 非線形な世界 by 大野克嗣：大野さん独自の視点で描かれた素晴らしい本。特に脚注がw
4. カオスの中の秩序—乱流の理解へ向けて by P. ペルジェ： 最初これで勉強しました。良
書です。
5. 非線形動力学とカオス—トポロジカルなアプローチ (Frontiers in Science) An Experimental
Approach to Nonlinear Dynamics and Chaos/Book and Disk (Studies in Nonlinearity) by Nicholas B.
Tufillaro Tyler Abbot and Jeremiah Reilly : Java appletもついていて、好きな入門書です。
6. Chaos in Dynamical Systems by E.Ott.
References: e.g.