1 Introduction 1
2 The Klein-Gordon equation below the ground state energy 17
2.1 Basic existence theory 20
2.2 Stationary solutions,ground state 29
2.3 The Payne-Sattinger criterion,regions ？ 34
2.4 Scattering in ？ 37
2.5 Strichartz estimates for Klein-Gordon equations 63
2.6 Summary and conclusion 77
3 Above the ground state energy Ⅰ:Near Q 79
3.1 Energy landscape 80
3.2 Center,stable,and unstable manifolds in hyperbolic dynamics 85
3.3 Center-stable manifolds via the Lyapunov-Perron method 108
3.4 Dispersive estimates for the perturbed linear evolution 117
3.5 The center-stable manifold for the radial cubic NLS in R3 130
3.6 Summary and conclusion 143
4 Above the ground state energy Ⅱ:Moving away from Q 145
4.1 Nonlinear distance function,eigenmode dominance,ejection 145
4.2 J and K0,K2 above the ground state energy 158
4.3 The one-pass theorem 162
4.4 Summary and conclusion 170
5 Above the ground state energy Ⅲ:Global NLKG dynamics 173
5.1 Statement of the main results on global dynamics 174
5.2 The blowup/scattering dichotomy in the ejection case 177
5.3 Proofs of the main results 182
5.4 Summary and conclusion 188
6 Further developments of the theory 191
6.1 The nonradial cubic NLKG equation in R3 194
6.2 The one-dimensional NLKG equation 204
6.3 The cubic radial NLS equation in R3 218
6.4 The energy critical wave equation 232
References 241
Index 251