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
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