不变流形和色散型哈密顿发展方程

1 Introducton

2 The Klein-Gordon equation below the ground state energy

2.1 Basic existencetheory

2.2 Stationary solutions, ground state

2.3 The Payne-Sattinger criterion, regions

2.5 Strichartz estimates for Klein-Gordon equations

2.6 Summary andconclusion

3 Above the ground state energy I: Near Q

3.1 Energylandscape

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 perturbedlinear evolution

3.5 The center-stable manifold for the radial cubic NLS in R3

3.6 Summary andconclusion

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 Theone-pass theorem

4.4 Summary and conclusion

5 Above the ground state energy III: Global NLKG dynamics

5.1 Statement ofthe main results on globaldynamics

5.2 The blowup/scattering dichotomy in the ejection case

5.3 Proofs ofthe main results

5.4 Summaryandconclusion

6 Further developments ofthe theory

6.1 The nonradial cubic NLKG equation in IR3

6.2 The one-dimensionalNLKG equation

6.3 The cubic radialNLS equationir1R3

6.4 The energy criticalwaveequation

Index

Erwin Bolthausen (Managing Editorl, Freddy Delbaen, Thomas Kappeler [Managing Editor), Christoph Schwab, Michael Struwe, Gisbert Wustholz　　Mathematics in Zurich has a long and distinguished tradition, in which the writing of lecture notes volumes and research monographs plays a prominent part. The Zurich Lectures in Advonced Mathematics seriesaims to make some of these publications better known to a wider audience. The series has three main con- stituents: lecture notes on advanced topics given by internationally renowned experts, graduate text books designed for the joint graduate program in Mathematics of the ETH and the Universit\/ of Zurich, as well as contributions from researchers in residence at the mathematics research institute, FIM-ETH. Moderately　　priced, concise and lively in style, the volumes of this series will appeal to researchers and students alike, who seek an informed introduction to important areas of current research.

《不变流形和色散型哈密顿发展方程》是一部分析学经典专著，以作者的最新研究为蓝本，证明基于两方面：基态的变分结构和这些态附近的非线性双曲动力学，这两方面的交互作用。本书适于为数学专业和物理专业的研究生和科研人员。书中详尽地呈现了三维中的Klein-Gordon三次方程，包括自由方程的Strichartz估计推导，和集中紧性争论导致的散射。
　　目次：基态能量以下的Klein-Gordon方程；基态能量Ⅰ之上，临近Q；基态能量Ⅱ之上，远离Q；基态能量Ⅲ之上：全局NLKG动力；该理论的更深研究。
　　《不变流形和色散型哈密顿发展方程》读者对象：本书适用于偏微分方程和数学物理方向的研究生和科研人员。