Complex Hamiltonian Dynamics

Front Cover
Springer Science & Business Media, Apr 3, 2012 - Science - 256 pages

This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems.


The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) research oriented problems provide many opportunities to deepen the reader’s insights into specific aspects of the subject matter.

Addressing a broad audience of graduate students, theoretical physicists and applied mathematicians, this text combines the benefits of a reference work with those of a self-study guide for newcomers to the field.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Chapter 1 Introduction
1
Chapter 2 Hamiltonian Systems of Few Degrees of Freedom
13
Chapter 3 Local and Global Stability of Motion
40
Chapter 4 Normal Modes Symmetries and Stability
63
Chapter 5 Efficient Indicators of Ordered and Chaotic Motion
91
Chapter 6 FPU Recurrences and the Transition from Weak to Strong Chaos
133
Chapter 7 Localization and Diffusion in Nonlinear OneDimensional Lattices
165
Chapter 8 The Statistical Mechanics of Quasistationary States
191
Chapter 9 Conclusions Open Problems and Future Outlook
221
References
239
Index
253
Copyright

Other editions - View all

Common terms and phrases