单摆：共振层、分岔树到混沌 (英文版) Resonance and Bifurcation to Chaos in Pendulum

样章

作者：

Albert C.J.Luo（罗朝俊）

定价：

99.00 元

版面字数：

290.000千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2017年

ISBN：

978-7-04-048004-7

物料号：

48004-00

出版时间：

2017-10-09

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

动力系统

暂无

前辅文
- 1 Resonance and Hamiltonian Chaos
  - 1.1 Stochastic layers
    - 1.1.1 Definitions
    - 1.1.2 Approximate criteria
  - 1.2 Resonant separatrix layers
    - 1.2.1 Layer dynamics
    - 1.2.2 Approximate criteria
  - References
- 2 Hamiltonian Chaos in Pendulum
  - 2.1 Resonance conditions
    - 2.1.1 Conservative system
    - 2.1.2 Resonance and energy increments
  - 2.2 Stochastic layers
  - 2.3 Resonant layers
    - 2.3.1 Librational resonant layers
    - 2.3.2 Rotational resonant layers
  - 2.4 Numerical simulations
  - References
- 3 Parametric Chaos in Pendulum
  - 3.1 Resonance and energy increment
    - 3.1.1 Libration
    - 3.1.2 Rotation
  - 3.2 Parametric stochastic layers
    - 3.2.1 Analytic predictions
    - 3.2.2 Numerical predictions
    - 3.2.3 Illustrations
    - 3.2.4 Numerical simulations
  - 3.3 Parametric resonant layers
    - 3.3.1 Approximate predictions
    - 3.3.2 Numerical illustrations
  - References
- 4 Nonlinear Discrete Systems
  - 4.1 Definitions
  - 4.2 Fixed points and stability
  - 4.3 Stability switching theory
  - 4.4 Bifurcation theory
  - References
- 5 Periodic Flows in Continuous Systems
  - 5.1 Discretization-based methods
  - 5.2 Discrete Fourier series
  - References
- 6 Periodic Motions to Chaos in Pendulum
  - 6.1 Periodic motions in pendulum
    - 6.1.1 Implicit discretization
    - 6.1.2 Periodic motions
  - 6.2 Bifurcation trees to chaos
    - 6.2.1 Period-1 motions to chaos
    - 6.2.2 Period-3 motions to chaos
    - 6.2.3 Period-5 motions to chaos
  - 6.3 Frequency-amplitude characteristics
    - 6.3.1 Period-1 to period-4 motions
    - 6.3.2 Period-3 to period-6 motions
    - 6.3.3 Symmetric to asymmetric period-5 motions
  - 6.4 Bifurcation trees varying with excitation amplitude
    - 6.4.1 Non-travelable period-1 motions to chaos
    - 6.4.2 Non-travelable period-3 motions to chaos
    - 6.4.3 Travelable period-1 motions to chaos
    - 6.4.4 Travelable period-2 motions to chaos
  - 6.5 Numerical simulations
    - 6.5.1 Non-travelable periodic motions
    - 6.5.1.1 Period-1 to period-4 motions
    - 6.5.1.2 Period-3 to period-6 motions
    - 6.5.1.3 Period-5 motions
    - 6.5.2 Travelable periodic motions
    - 6.5.2.1 Travelable period-1 to period-2 motions
    - 6.5.2.2 Travelable period-2 to period-8 motions
  - References
Subject Index