文档介绍：DIFFERENTIAL EQUATIONS: GEOMETRIC THEORY
SECOND EDITION
PURE AND APPLIED MATHEMATICS
A Series of Texts and Monographs
Editedby: R. COURANT • •. STOKER
VOLUME VI
DIFFERENTIAL EQUATIONS:
GEOMETRIC THEORY
SECOND EDITION
SOLOMON LEFSCHETZ
PRINCETON UNIVERSITY
THE NATIONAL UNIVERSITY OF MEXICO
AND
RIAS, BALTIMORE
U BLISHERS
a division of John Wiley & Sons, New York •London
ALL RIGHTS RESERVED
Library of Congress Catalog Card Number 62-21884
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Preface
The surprisingly warm reception which greeted the author's
monograph Lectures on Differential Equations (Princeton Univer-
sity Press 1946) provided the incentive to enlarge the monograph
to the present volume. However, the general plan has remained
the same, and readers acquainted with the monograph will
readilyfind their way here. We continue to lean more heavily
than ever on vectors and matrices and to utilize topological
notions.
In relation to the monograph the present scheme is the follow-
ing. The first four chapters are about as before: more or less pre-
paratory and standard. The next three deal with point stability
and contain much additional information on the work of Lia-
punov and his Soviet essors, notably on the so-called direct
method of Liapunov. With Chapter VIII —periodicsolutions
—then dimensional part is concluded. This chapter is admittedly
fragmentary, but then this is unavoidable, given the present state
of this general question. The remaining chapters deal with two-
dimensional systems. Two chapters are devoted to The results of
and Bendixson: critical points, the index, behavior at
infinity, some special systems. An introduction is also given to the
important notion of structural stability and the contributions of
Andronov-Pontrjagin and DeBaggis. The last two chapters deal
with equations of the second order: notably the recent work. of
Cartwright-Littlewood, of Levinson-Smith and of Levinson, the
application of the