Introduction to chaos : physics and mathematics of chaotic phenomena
Introduction to chaos : physics and mathematics of chaotic phenomena
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混沌导论：混沌现象的物理和数学
DOI：
10.5860/choice.36-6327
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
馬場 良和
中科院分区：
文献类型：
--
作者：
長島 弘幸;馬場 良和
什么是混乱？自然界混沌的特征LI-YORKE混沌、拓扑熵和LYAPUNOV NUMBER LI-YORKE定理和Sharkovski定理：LI-YORKE定理Sharkovski定理周期轨道：周期轨道数轨道稳定性LI-YORKE定理（续）LI-YORKE混沌的乱集和可观测性：Nathanson的例子LI-YORKE混沌的可观测性拓扑熵可观测混沌与Lyapunov数轨道的密度不变测度Lyapunov数摘要混沌的路径Pitchfork分叉与Feigenbaum路径Pitchfork分叉的条件窗口现实系统中的间断混沌保守系统与耗散系统中的吸引子与庞加莱剖面Lyapunov数与体积的变化吸引子Hausdorff维数的构造广义维数与分形相关维数的评价Lyapunov数的评价全局谱- If(a)方法附录logistic映射的周期解莫比乌斯函数与反演公式可数集与不可数集上限与下限Lebsgue测度正规数初值有限分数的周期轨道delta函数logistic映射的周期3窗口从哪里开始？牛顿法如何评价拓扑熵不变测度的例子广义维数Dq在q中单调递减鞍点法双摆的混沌van der Pol方程的奇异点与极限环Rossler模型的奇异点参考解INDEX
WHAT IS CHAOS? Characteristics of chaos Chaos in nature LI-YORKE CHAOS, TOPOLOGICAL ENTROPY, AND LYAPUNOV NUMBER Li-Yorke theorem and Sharkovski theorem: Li-Yorke's theorem Sharkovski's theorem Periodic orbits: Number of periodic orbits Stability of orbits Li-Yorke theorem (continued) Scrambled set and observability of Li-Yorke chaos: Nathanson's example Observability of Li-Yorke chaos Topological entropy Density of orbits: Observable chaos and Lyapunov number Denseness of orbits Invariant measure Lyapunov number Summary ROUTE TO CHAOS Pitchfork bifurcation and Feigenbaum route Conditions for pitchfork bifurcation Windows Intermittent chaos CHAOS IN REALISTIC SYSTEMS Conservative system and dissipative system Attractors and Poincare section Lyapunov numbers and change of volume Construction of attractor Hausdorff dimension, generalized dimension and fractal Evaluation of correlation dimension Evaluation of Lyapunov number Global spectrum-the If(a) method APPENDICES Periodic solutions of the logistic map Mobius function and inversion formula Countable sets and uncountable sets Upper limit and lower limit Lebsgue measure Normal numbers Periodic orbits with finite fraction initial value The delta-function Where does period 3 window begin in logistic map? Newton method How to evaluate topological entropy Examples of invariant measure Generalized dimension Dq is monotonically decreasing in q Saddle point method Chaos in double-pendulum Singular points and limit cycle of van der Pol Equation Singular points of the Rossler model REFERENCES SOLUTIONS INDEX