Classics in Mathematics

By: N.P. Bhatia, G.P. Szegö

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Paperback | 10 January 2002

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248 Pages

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22.86 x 15.24 x 1.27

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From the reviews:
"This is an introductory book intended for beginning graduate students or, perhaps advanced undergraduates. ... 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."
Mathematical Reviews, 1972
"The exposition is remarkably clear, definitions are separated explicitly, theorems are often provided together with the motivation for changing one or other hypothesis, as well as the relevance of certain generalisations... This study is an excellent review of the current situation for problems of stability of the solution of differential equations. It is addressed to all interested in non-linear differential problems, as much from the theoretical as from the applications angle."
Bulletin de la Societe Mathematique de Belgique, 1975

Industry Reviews

From the reviews: "The book presents a systematic treatment of the theory of dynamical systems and their stability written at the graduate and advanced undergraduate level. ! The book is well written and contains a number of examples and exercises." (Alexander Olegovich Ignatyev, Zentralblatt MATH, Vol. 993 (18), 2002)

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Dynamical Systems
Definition and Related Notation
Examples of Dynamical Systems Notes and References
Elementary Concepts
Invariant Sets and Trajectories
Critical Points and Periodic Points
Trajectory Closures and Limit Sets
The First Prolongation and the Prolongational Limit Set Notes and References
Recursive Concepts
Definition of Recursiveness
Poisson Stable and Non-wandering Points
Minimal Sets and Recurrent Points
Lagrange Stability and Existence of Minimal Sets Notes and References
Dispersive Concepts
Unstable and Dispersive Dynamical Systems
Parallelizable Dynamical Systems Notes and References
Stability Theory
Stability and Attraction for Compyct Sets
Liapunov Functions: Characterization of Asymptotic Stability
Topological Properties of Regions of Attractions
Stability and Asymptotic Stability of Closed Sets
Relative Stability Properties
Stability of a Motion and Almost Periodic Motions Notes and References
Flow near a Compact Invariant Set
Description of Flow near a Compact Invariant Set
Flow near a Compact Invariant Set (Continues) Notes and References
Higher Prolongations
Definiton of Higher Prolongations
Absolute Stability
Generalized Recurrence Notes and References
E1 Liapunov Functions for Ordinary Differential Equations
Introduction
Preliminary Definitions and Properties
Local Theorems
Extension Theorems
The Structure of Liapunov Functions
Theorems Requiring Semidefinite Derivatives
On the Use of Higher Derivaties of a Liapunov Function Notes and References
Non-continuous Liapunov Functions for Ordinary Differential Equations
Introduction
A Characterization of Weak Attractors
Piecewise Differentialbe Liapunov Functions
Local Results
Extension Theorems
Non-continuous Liapunov Functions on the Region of Weak Attraction
Notes and References
References Author
Index Subject
Index
Table of Contents provided by Publisher. All Rights Reserved.

Classics in Mathematics

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