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Qualitative Theory of Differential Equations

V. V. Nemytskii and V. V. Stepanov
Dover Publications
Publication Date: 
Number of Pages: 
Dover Books on Advanced Mathematics
We do not plan to review this book.


Preface to the English Language Edition
Part One.
Chapter 1. Existence and Continuity Theorems
  1. Existence theorems
  2. Certain uniqueness and continuity theorems
  3. Dynamical systems defined by a system of differential equations
  4. Regular families of integral curves
  5. Fields of linear elements
Chapter 2. Integral Curves of a System of Two Differental Equations
  1. General properties of integral curves in the plane
  2. Trajectories on a torus
  3. Geometrical classification of singular points
  4. Analytic criteria for various types of singular points
Chapter 3. Systems of n Differential Equations (the Asymptotic Behaviour of Solutions)
  1. Introduction
  2. Qualitative study of systems with constant coefficients and of reducible systems
Chapter 4. A Study of Neighborhoods of Singular Points and of Periodic Solutions of Systems of n Differential Equations
  1. Singular points in the analytic case
  2. Lyapunov stability
  3. The behavior of the trajectories in the neighborhood of a closed trajectory
  4. The method of surfaces of section
  Bibliography to Part One
  Appendix to Part One: Problems of the qualitative Theory of Differential Equations (By V. V. Nemickii)
  Index to Part One
Part Two.
Chapter 5. General Theory of Dynamical Systems
  1. Metric spaces
  2. General properties and local structure of dynamical systems
  3. omega- and alpha-limit points
  4. Stability acording to Poisson
  5. Regional recurrence. Central motions
  6. Minimal center of attraction
  7. Minimal sets and recurrent motions
  8. Almost periodic motions
  9. Asymptotic trajectories
  10. Completely unstable dynamical systems
  11. Dynamical systems stable according to Lyapunov
Chapter 6. Systems with an Integral Invariant
  1. Definition of an integral invariant
  2. Measure of Carathéodory
  3. Recurrence theorems
  4. Theorms of E. Hopf
  5. G. D. Birkihoff's ergodic theorem
  6. Supplement to the ergodic theorem
  7. Statistical ergodic theorems
  8. Generalizations of the ergodic theorem
  9. Invariant measures of an arbitrary dynamical system
  Bibliography to Part Two
  Index to Part Two