Stability theory of dynamical systems
著者
書誌事項
Stability theory of dynamical systems
（Classics in mathematics）
Tokyo : Springer, c2002
- : pbk
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注記
Includes bibliographical references and index
"Reprint of the 1970 edition"
Originally published: Berlin : Springer , 1970.(Grundlehren der mathematischen Wissenschaften ; v. 161)
内容説明・目次
内容説明
Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."
目次
I. Dynamical Systems 1. Definition and Related Notation 2. Examples of Dynamical Systems Notes and References II. Elementary Concepts 1. Invariant Sets and Trajectories 2. Critical Points and Periodic Points 3. Trajectory Closures and Limit Sets 4. The First Prolongation and the Prolongational Limit Set Notes and References III Recursive Concepts 1. Definition of Recursiveness 2. Poisson Stable and Non-wandering Points 3. Minimal Sets and Recurrent Points 4. Lagrange Stability and Existence of Minimal Sets Notes and References IV Dispersive Concepts 1. Unstable and Dispersive Dynamical Systems 2. Parallelizable Dynamical Systems Notes and References V Stability Theory 1. Stability and Attraction for Compyct Sets 2. Liapunov Functions: Characterization of Asymptotic Stability 3. Topological Properties of Regions of Attractions 4. Stability and Asymptotic Stability of Closed Sets 5. Relative Stability Properties 6. Stability of a Motion and Almost Periodic Motions Notes and References VI Flow near a Compact Invariant Set 1. Description of Flow near a Compact Invariant Set 2. Flow near a Compact Invariant Set (Continues) Notes and References VII Higher Prolongations 1. Definiton of Higher Prolongations 2. Absolute Stability 3. Generalized Recurrence Notes and References VIII E1 Liapunov Functions for Ordinary Differential Equations 1. Introduction 2. Preliminary Definitions and Properties 3. Local Theorems 4. Extension Theorems 5. The Structure of Liapunov Functions 6. Theorems Requiring Semidefinite Derivatives 7. On the Use of Higher Derivaties of a Liapunov Function Notes and References IX Non-continuous Liapunov Functions for Ordinary Differential Equations 1. Introduction 2. A Characterization of Weak Attractors 3. Piecewise Differentialbe Liapunov Functions 4. Local Results 5. Extension Theorems 6. Non-continuous Liapunov Functions on the Region of Weak Attraction Notes and References References Author Index Subject Index
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