Continuous Flows in the Plane

  • Anatole Beck

Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 201)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Anatole Beck
    Pages 1-5
  3. Anatole Beck
    Pages 6-33
  4. Anatole Beck
    Pages 34-58
  5. Anatole Beck
    Pages 59-99
  6. Anatole Beck
    Pages 100-135
  7. Anatole Beck
    Pages 136-174
  8. Anatole Beck
    Pages 175-201
  9. Anatole Beck
    Pages 202-224
  10. Anatole Beck
    Pages 225-278
  11. Anatole Beck
    Pages 279-314
  12. Back Matter
    Pages 415-462

About this book

Introduction

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 equations, and the subject has grown around this nucleus. It has developed now to a point where it is fully capable of standing on its own feet as a branch of Mathematics studied for its intrinsic interest and beauty, and since the publication of Topological Dynamics by Gottschalk and Hedlund, it has been the subject of widespread study in its own right, as well as for the light it sheds on differential equations. The Bibliography for Topological Dyna­ mics by Gottschalk contains 1634 entries in the 1969 edition, and progress in the field since then has been even more prodigious. The study of dynamical systems is an idealization of the physical studies bearing such names as aerodynamics, hydrodynamics, electrodynamics, etc. We begin with some space (call it X) and we imagine in this space some sort of idealized particles which change position as time passes.

Keywords

Differentialgleichung Flows Plane Topologische Dynamik equation mathematics

Authors and affiliations

  • Anatole Beck
    • 1
  1. 1.University of WisconsinMadisonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-65548-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1974
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-65550-0
  • Online ISBN 978-3-642-65548-7
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site