力学系の記事

Diagram showing the periodic orbit of a mass-spring system in simple harmonic motion. (The velocity and position axes have been reversed from the standard convention in order to align the two diagrams)

相空間と微分方程式動的システムの視覚的解析

相空間微分方程式相図力学系

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Visual representation of a strange attractor.[1] Another visualization of the same 3D attractor is this video. Code capable of rendering this is available.

アトラクタとは何か力学系における状態の収束とカオス理論

アトラクタ力学系カオス理論ストレンジアトラクタ

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A set of dynamical systems. Top left: a cellular automaton. Top center: Exterior billiards. Top right a constrained 3-body problem. Bottom left a Poincare section of a Standard map (chaos arise in the dotted regions). Middle bottom: a chaotic Dynamical billiards (a symptom of chaos here are the trajectories filling the configuration space). Bottom right: A geodesic flow such as light on a surface, trajectories are geodesics i.e. minimum paths, in this case the phase space is a torus (stable orbits arise when the periods are rational, if irrational that is a path to chaos).

力学系時間とともに変化するシステムの数学的記述

力学系カオス理論分岐理論ポアンカレ写像

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The behavior of the logistic map is shown in Cobweb plot form. The animation shows the change in behavior as the parameter (r in the figure) is increased from 1 to 4, starting from an initial function value of 0.2.

ロジスティック写像単純な数式が導くカオスと秩序の世界

ロジスティック写像カオス理論分岐図周期倍分化

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