Contributions to the Theory of Nonlinear Oscillations, Volume III

by Solomon Lefschetz

Overview

Classic contributions to the theory of nonlinear oscillations from the acclaimed Annals of Mathematics Studies series

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century.

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Product Details

ISBN-13:	9780691079110
Publisher:	Princeton University Press
Publication date:	01/21/1956
Series:	Annals of Mathematics Studies , #36
Pages:	296
Product dimensions:	8.25(w) x 11.00(h) x (d)

Table of Contents

• Frontmatter, pg. i
• PREFACE, pg. v
• CONTENTS, pg. vii
• I. A ROTATED VECTOR APPROACH TO THE PROBLEM OP STABILITY OP SOLUTIONS OF PENDULUM-TYPE EQUATIONS, pg. 1
• II. ASYMPTOTICALLY AUTONOMOUS DIFFERENTIAL SYSTEMS, pg. 17
• III. NONLINEAR DIFFERENTIAL EQUATIONS SYSTEMS, pg. 31
• IV. ON A NON-LINEAR DIFFERENTIAL EQUATION CONTAINING A SMALL PARAMETER, pg. 57
• V. CRITICAL POINTS AT INFINITY AND FORCED OSCILLATION, pg. 85
• VI. ON CERTAIN CRITICAL POINTS OF A DIFFERENTIAL SYSTEM IN THE PLANE, pg. 127
• VII. ON THE TOTAL NUMBER OF SINGULAR POINTS AND LIMIT CYCLES OF A DIFFERENTIAL EQUATION, pg. 137
• VIII. BANACH SPACES AND THE PERTURBATION OF ORDINARY DIFFERENTIAL EQUATIONS, pg. 173
• IX. A FIXED POINT THEOREM, pg. 197
• X. PERTURBATION THEOREMS FOR NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS, pg. 207
• XI. A NOTE ON THE EXISTENCE OF PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS, pg. 237
• XII. AN INVARIANT SURFACE THEOREM FOR A NON-DEGENERATE SYSTEM, pg. 243
• XIII. AN APPLICATION OP PERIODIC SURFACES (SOLUTION OF A SMALL DIVISOR PROBLEM), pg. 257
• XIV. REPEATING SOLUTIONS FOR A DEGENERATE SYSTEM, pg. 261
• XV. BOUNDS FOR PERIODS OF PERIODIC SOLUTIONS, pg. 269
• XVI. ONE-DIMENSIONAL REPEATING CURVES IN THE NON-DEGENERATE CASE, pg. 277
• Backmatter, pg. 288