| 《非线性物理科学：连续动力系统（英文版）》首次展示动力系统的周期流和混沌的解析解，给出连续动力系统的稳定性和分叉的详尽分类，首次讨论具有高阶奇异性的稳定性和分叉理论，分析连续动力系统流的全局横截性，给出非线性哈密顿系统混沌的解析判据，读者群大，应用面广，直观、简洁、易读。 |
| Preface Chapter 1 Linear Systems and Stab 1.1 Linear systems with distinct eigenvalues 1.2 Operator exponentials 1.3 Linear systems with repeated eigenvalues 1.4 Nonhomogeneous linear systems 1.5 Linear systems with periodic coefficients 1.6 Stability and boundary 1.7 Lower-dimensional linear systems 1.7.1 One-dimensional linear systems 1.7.2 Planar linear systems 1.7.3 Three-dimensional linear systems References Chapter 2 Stability Switching and Bifurcation 2.1 Continuous dynamical systems 2.2 Equilibriums and stabilit 2.3 Bifurcation and stability switching 2.3.1 Stability and switching 2.3.2 Bifurcations 2.3.3 Lyapunov functions and stability References Chapter 3 Analytical Periodic Flows and Chaos 3.1 Analytical periodic flows 3.1.1 Autonomous nonlinear systems 3.1.2 Periodically forced nonlinear systems 3.2 Nonlinear vibration systems 3.2.1 Free vibration systems 3.2.2 Periodically forced vibration systems 3.3 A periodically forced Duffing oscillator References Chapter 4 Global Transversality and Chaos 4.1 Nonlinear dynamical systems 4.2 Local and global flows 4.3 Global transversal 4.4 Global tangency 4.5 Perturbed Hamiltonian systems 4.6 Two-dimensional Hamiltonian systems 4.7 First integral quantity increment 4.8 A damped Duffing oscillator 4.8.1 Conditions for global transversality and tangency 4.8.2 Poincare mapping and mapping structures 4.8.3 Bifurcation scenario 4.8.4 Numericalillustrations References Chapter 5 Resonance and Hamiltonian Chaos 5.1 Stochastic layers 5.1.1 Definitions 5.1.2 Approximate criteria 5.2 Resonant separatrix layers 5.2.1 Layer dynamics 5.2.2 Approximate criteria 5.3 A periodically forced Duffing oscillator 5.3.1 Approximate predictions 5.3.2 Numericalillustrations 5.4 Concluding remarks References Index |
内容加载中，请稍后...
商品评论（0条）