chaos

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

Edward Lorentz

Lorentz Attractor

ρ=28, σ = 10 and β = 8/3

Lorentz equation

Driven Duffing’s Oscillator

HTTTTHTHTHHTHTHHHHHH,,,,,,,

Smale’s horseshoe

Baker’s transformation

Homoclinic tangle

{!n}! {!n+1}

{xn}! {xn+1}

B

f

! !

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.