This volume can serve as an introduction and a reference source on spectral and inverse spectral theory of Jacobi operators (i.e., second order symmetric difference operators) and applications of those theories to the Toda and Kac-van Moerbeke hierarchy. Beginning with second order difference equations, the author develops discrete Weyl-Titchmarsh-Kodaira theory, covering all classical aspects, such as Weyl $m$-functions, spectral functions, the moment problem, inverse spectral theory, and uniqueness results.Teschl then investigates more advanced topics, such as locating the essential, absolutely continuous, and discrete spectrum, subordinacy, oscillation theory, trace formulas, random operators, almost periodic operators, (quasi-)periodic operators, scattering theory, and spectral deformations. Utilizing the Lax approach, he introduces the Toda hierarchy and its modified counterpart, the Kac-van Moerbeke hierarchy. Uniqueness and existence theorems for solutions, expressions for solutions in terms of Riemann theta functions, the inverse scattering transform, Backlund transformations, and soliton solutions are derived. This text covers all basic topics of Jacobi operators and includes recent advances. It is suitable for use as a text at the advanced graduate level.
Numerous inroads to this research exist for the advanced student. This book offers glimpses into the field with the aim that the results presented illuminate the beauty & excitement to be found.
Dynamics & Stochastics: Festschrift in Honour of M.S. Keane
书名原文:Mathematics of models:Continuous and discrete dynamical systems
Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.
A New Mathematical Framework for the Study of Linkage and Selection
This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications.
"This book describes methods that reveal its structures and dynamics.
This book presents a new theory on the transition to dynamical chaos for two-dimensional nonautonomous, and three-dimensional, many-dimensional and infinitely-dimensional autonomous nonlinear dissipative systems of differential equations ...
... and José Seade, Editors, Geometry and dynamics, 2005 Ravi Vakil, Editor, Snowbird lectures in algebraic geometry, 2005 Michael Entov, Yehuda Pinchover, and Michah Sageev, Editors, Geometry, spectral theory, groups, and dynamics, ...
Global Structural Stability of Flows on Open Surfaces