1 Introduction
2 The Klein—Gordon equation below the ground state energy
2.1 Basic existence theory
2.2 Stationary solutions， ground state
2.3 The Payne—Sattinger criterion， regions □S±
2.4 Scattering in □S+
2.5 Strichartz estimates for Klein—Gordon equations
2.6 Summary and conclusion
3 Above the ground state energy Ⅰ： Near Q
3.1 Energy landscape
3.2 Center， stable， and unstable manifolds in hyperbolic dynamics
3.3 Center—stable manifolds via the Lyapunov—Perron method
3.4 Dispersive estimates for the perturbed linear evolution
3.5 The center—stable manifold for the radial cubic NLS in R3
3.6 Summary and conclusion
4 Above the ground state energy Ⅱ： Moving away from Q
4.1 Nonlinear distance function， eigenmode dominance， ejection
4.2 J and Ko， K2 above the ground state energy
4.3 The one—pass theorem
4.4 Summary and conclusion
5 Above the ground state energy Ⅲ： Global NLKG dynamics
5.1 Statement of the main results on global dynamics
5.2 The blowup／scattering dichotomy in the ejection case
5.3 Proofs of the main results
5.4 Summary and conclusion
6 Further developments of the theory
6.1 The nonradial cubic NLKG equation in R3
6.2 The one—dimensional NLKG equation
6.3 The cubic radial NLS equation in R3
6.4 The energy criticalwave equation
References
Index
