Qualitative theory of differential equations

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Qualitative theory of differential equations / by V.V. Nemytskii and V.V. Stepanov

資料種別:

図書

出版情報:

Princeton, N.J. : Princeton University Press, 1960

形態:

viii, 523 p. ; 24 cm

シリーズ名:

Princeton mathematical series ; 22 <BA00109433>

著者名:

ISBN:

9780691080208 [0691080208]

書誌ID:

BA00759927

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

主題:

微分方程式

言語:

英語

目次情報:

Preface to the English Language Edition

Existence and Continuity Theorems / Part One：

Existence theorems / 1：

Certain uniqueness and continuity theorems / 2：

Dynamical systems defined by a system of differential equations / 3：

Regular families of integral curves / 4：

Fields of linear elements / 5：

Integral Curves of a System of Two Differental Equations / Chapter 2：

General properties of integral curves in the plane

Trajectories on a torus

Geometrical classification of singular points

Analytic criteria for various types of singular points

Systems of n Differential Equations (the Asymptotic Behaviour of Solutions) / Chapter 3：

Introduction

Qualitative study of systems with constant coefficients and of reducible systems

A Study of Neighborhoods of Singular Points and of Periodic Solutions of Systems of n Differential Equations / Chapter 4：

Singular points in the analytic case

Lyapunov stability

The behavior of the trajectories in the neighborhood of a closed trajectory

The method of surfaces of section

Bibliography to Part One

Appendix to Part One

Problems of the qualitative Theory of Differential Equations / V. V. Nemickii

Index to Part One

General Theory of Dynamical Systems / Part Two：

Metric spaces

General properties and local structure of dynamical systems

omega- and alpha-limit points

Stability acording to Poisson

Regional recurrence. Central motions

Minimal center of attraction / 6：

Minimal sets and recurrent motions / 7：

Almost periodic motions / 8：

Asymptotic trajectories / 9：

Completely unstable dynamical systems / 10：

Dynamical systems stable according to Lyapunov / 11：

Systems with an Integral Invariant / Chapter 6：

Definition of an integral invariant

Measure of Caratheodory

Recurrence theorems

Theorms of E. Hopf

G. D. Birkihoff's ergodic theorem

Supplement to the ergodic theorem

Statistical ergodic theorems

Generalizations of the ergodic theorem

Invariant measures of an arbitrary dynamical system

Bibliography to Part Two

Index to Part Two

Preface to the English Language Edition

Existence and Continuity Theorems / Part One：

Existence theorems / 1：

Certain uniqueness and continuity theorems / 2：

Dynamical systems defined by a system of differential equations / 3：

Regular families of integral curves / 4：

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