Complex Hamiltonian Dynamics

ISBN-13: 9783642273049 / Angielski / Twarda / 2012 / 256 str.

Tassos Bountis; Haris Skokos

Opis

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.

Recenzje

From the reviews:

"The monograph is devoted to some recent developments in Hamiltonian dynamical systems, focusing on the transitional regimes between regular and chaotic motion. ... The exposition is very well motivated and brings together many topics from different fields. ... The book will be useful for researchers in this area and potentially as a supplementary reading for an advanced graduate Physics course." (Nikola P. Petrov, Mathematical Reviews, March, 2014)

Spis treści

Hamiltonian Systems of Few Degrees of Freedom.- Equilibrium Points, Periodic Orbits and Local Stability.- Efficient Indicators of Stable and Chaotic Motion.- FPU Recurrences and the Transition from Weak to Strong Chaos.- Localization and Diffusion in Nonlinear 1-Dimensional Lattices.- The Statistical Mechanics of Quasi-Stationary States.- Conclusion, Open Problems and Future Outlook.