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 ？

2.4 Scattering in ？

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 K0,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 critical wave equation

References

Index