Continuous Flows in the Plane
Topological Dynamics has its roots deep in the theory of differential equations, specifically in that portion called the "qualitative theory". The most notable early work was that of Poincare and Bendixson, regarding stability of solutions of differential
- PDF / 35,846,975 Bytes
- 474 Pages / 430.92 x 649.08 pts Page_size
- 104 Downloads / 254 Views
Band 201
Herausgegeben von S. S. Chern J. L. Doob J. Douglas, jr. A. Grothendieck E. Heinz F. Hirzebruch E. Hopf W. Maak S. MacLane W. Magnus M. M. Postnikov F. K. Schmidt D. S. Scott K. Stein
Geschiiftsfuhrende Herausgeber B. Eckmann B. L. van der Waerden
Anatole Beck
Continuous Flows in the Plane With the Assistance of
Jonathan and Mirit Lewin
Springer-Verlag Berlin Heidelberg New York 1974
Professor Anatole Beck University of Wisconsin, Madison, Wisconsin, USA
Dr. Jonathan and Dr. Mirit Lewin Ben Gurion University of the Negev, Beer Sheva, Israel
With 47 Figures
AMS Subject Classifications (1970) Primary 54 H20, 34 C 35, 54 H 15, 57 E 25 Secondary 54H25, 57E05, 57E20, 58F99, 70G99
ISBN-13: 978-3-642-65550-0 e-ISBN-13: 978-3-642-65548-7 DOl: 10.1007/978-3-642-65548-7 This work is subject to copyright. All rights are reserved, whether the whole or part of tbe material is concerned, specifically those of translation, reprinting. fe-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer·Verlag Berlin· Heidelberg 1974. Library of Congress Catalog Card Number 73·11952. Softcover reprint of the hardcover 1st edition 1974
Dedicated to the memory of my mother MINNIE BECK BORNSTEIN
March 41904 She made of her life a gift to those she loved. Without her many sacrifices, this book might never have been written
.;,,~~ C'l'l!J~ pM"~ •;"1V11~ C'111Vi:J
Nl~"~ ?'M nWN
•••
il'??il"
;""
"!J~ ;,; un
PROLOGUE Der junge Alexander eroberle Indien Er allein?
The time of publishing a book is a time to remember and to give thanks. A time to remember all those who by their help have made the book possible and to give thanks for that help. In this case, where the book represents sixteen years of research built on an education of twenty years, the list of those who by their efforts and kindnesses have fostered the education, the research, and the writing of the book runs to many hundreds. Of these, a few dozen have contributed so much that I could not allow the book to go to press without explicit acknowledgement of their assistance. I begin with my mother, whose contribution over the years was the greatest, and to whose memory this book is dedicated. Widowed at an early age with two young sons, she labored long hours at difficult and unrewarding work to make our educations possible. The price of those educations, to which she contributed unstintingly from her meager earnings, was high, for the accumulated damage to her health led her to an untimely death. Without her support, both financial and psychological, it is questionable whether I would have completed that education, without which this book would have been impossible. I am deeply conscious of my debt to my teachers, both in school and in the various universities I have attended. Of these, I
