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Publisher:

Dover Publications

Publication Date:

1989

Number of Pages:

523

Format:

Paperback

Series:

Dover Books on Advanced Mathematics

Price:

14.95

ISBN:

0486659542

Category:

Textbook

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 | ||||||||

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