Stability Theory of Dynamical Systems
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Stability Theory of Dynamical Systems: (Classics in Mathematics)

Stability Theory of Dynamical Systems: (Classics in Mathematics)

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About the Book

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 Société Mathématique de Belgique, 1975

Table of Contents:
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 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.- V. 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.- VII. Higher Prolongations.- 1. Definition of Higher Prolongations.- 2. Absolute Stability.- 3. Generalized Recurrence.- Notes and References.- VIII. ?1-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.- 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.


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Product Details
  • ISBN-13: 9783540427483
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 225
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 3540427481
  • Publisher Date: 10 Jan 2002
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Series Title: Classics in Mathematics


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