这是一本关于单摆共振层及其周期运动到混沌的著作。周期强迫振动摆是一个典型且常见的最简单的非线性振子，具有复杂和丰富的非线性动力学行为。虽然此类周期强迫振动摆是一个最简单的非线性动力系统，但要找到它的周期运动到混沌非常困难。并且这一周期强迫振动摆固有的复杂动力学行为远远超出了我们基于传统线性动力系统的想象。到目前为止，人们仍然不知道此类周期强迫振动钟摆的复杂运动及其物理学本质和数学理论，本书中所展示的结果将为探索周期强迫振动摆的复杂非线性动力学行为带来一些新颖观点。
Preface
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
6．5．2 Travelable periodic motions
References
Subject Index
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