Stability Theory of Dynamical Systems [Softcover reprint of the original 1st ed. 2002] 3540427481, 9783540427483

Table of contents :
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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

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