Local methods in nonlinear differential equations

Cover
	Local Methods in Nonlinear Differential Equations
	Introduction to the English Edition by Dr. Steven Wiggins
	Table of Contents
	Table of Contents
	Basic Notation
	Introduction
	Chapter I Foundations of the Local Method
	§1. Linear Inequalities in the Plane
	§2. Zeros of an Analytic Function
	§ 3. Level Curves of an Analytic Function
	Chapter II A System of Two Differential Equations
	§ 1. Simple Points and Elementary Singularities
	§2. Generalized Normal Forms
	§3. A Nonelementary Singular Point
	§4. On Distinguishing Between a Center and a Focus
	Chapter III The Normal Form of a System of n Differential Equations
	§1	. The Normalizing Transformation
	§2. The Integration and Classification of Normal Forms
	§3. Analytic Integral Sets
	§4. The Normal Form and Methods of Averaging
	Chapter IV On the Newton Polyhedron
	§ 1. A System of Differential Equations
	§2. Other Problems Using the Newton Polyhedron
	Chapter V Applications of the Normal Form in Mechanics
	§ 1. On the Motion of a Gyroscope in a Cardan Suspension
	§ 2.	On the Oscillations of a Satellite in the Plane of an Elliptical Orbit
	References
	Part II The Sets of Analyticity of a Normalizing Transformation
	Preface
	Table of Contents
	Basic Notation
	Introduction
	§ 1.	The Seminormal Form
	§ 2.	Questions of Convergence
	§ 3.	A Hamiltonian System
	§4. Families of Periodic Solutions
	§ 5. Integral Manifolds with Small Divisors
	Author’s Comments (1986)
	References
	Subject Index
	Backside Blurb