不变流形和色散型哈密顿发展方程（英文版）

不变流形和色散型哈密顿发展方程（英文版）
出版时间：2015年版
内容简介
　　Erwin Bolthausen （Managing Editorl， Freddy Delbaen， Thomas Kappeler [Managing Editor）， Christoph Schwab， Michael Struwe， Gisbert WustholzMathematics 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. Moderatelypriced， 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.
目录
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