## Table of contents for Stability theory of dynamical systems / N.P. Bhatia, G.P. Szego.

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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

Library of Congress subject headings for this publication:

Topological dynamics.

Stability.

Differential equations.