Stability Theory of Dynamical Systems

✍ Scribed by N.P. Bhatia, G.P. Szegö

• Publisher: Springer
• Year: 2002
• Tongue: English
• Leaves: 242
• Series: Classics in Mathematics
• Edition: Softcover reprint of the original 1st ed. 2002
• Category: Library

✦ Synopsis

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."

Topics
Theoretical, Mathematical and Computational Physics
Ordinary Differential Equations
Numerical and Computational Physics
Quantum Information Technology, Spintronics
Quantum Physics
Numerical Analysis

✦ Table of Contents

Cover

Authors

S Title

Stability Theory of Dynamical Systems

@ by Springer-Verlag, Berlin ·Heidelberg 1970
Library of Congress Catalog Card Number 70-126892

Dedicated To Sushiela and Emilia

Preface

Contents

Notation

Introduction

Chapter I Dynamical Systems
1. Definition and Related Notation
2. Examples of Dynamical Systems
Notes and References

Chapter 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

Chapter 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

Chapter IV Dispersive Concepts
1. Unstable and Dispersive Dynamical Systems
2. Parallelizable Dynamical Systems
Notes and References

Chapter V Stability Theory
1. Stability and Attraction for Compact Sets
2. Liapunov Functions : Characterization of Asymptotic Stability
3. Topological Properties of Regions of Attraction
4. Stability and Asymptotic Stability of Closed Sets
5. Relative Stability Properties
6 . Stability of a Motion and Almost Periodic Motions
Notes and References

Chapter VI Flow near a Compact Invariant Set
1. Description of Flow near a Compact Invariant Set
2. Flow near a Compact Invariant Set (Continued)
Notes and References

Chapter VII Higher Prolongations
1. Definition of Higher Prolongations
2. Absolute Stability
3. Generalized Recurrence
Notes and References

Chapter VIII C^4-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 Derivatives of a Liapunov Function
Notes and References

Chapter IX Non-continuous Liapunov Functions for Ordinary Differential Equations
1. Introduction
2. A Characterization of Weak Attractors
3. Piecewise Differentiable 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

Published Titles

Back Cover

✦ Subjects

Автоматизация;Теоретические основы автоматизации управления;