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Continuous Flows in the Plane

  • Book
  • © 1974

Overview

Authors:
  1. Anatole Beck

    1. University of Wisconsin, Madison, USA

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Introduction

    • Anatole Beck
    Pages 1-5

  3. Elementary Properties of Flows

    • Anatole Beck
    Pages 6-33

  4. Special Properties of Plane Flows

    • Anatole Beck
    Pages 34-58

  5. Regular and Singular Points

    • Anatole Beck
    Pages 59-99

  6. Reparametrization I

    • Anatole Beck
    Pages 100-135

  7. Reparametrization II

    • Anatole Beck
    Pages 136-174

  8. Existence Theorems I

    • Anatole Beck
    Pages 175-201

  9. Existence Theorems II

    • Anatole Beck
    Pages 202-224

  10. Algebraic Combinations of Flows I

    • Anatole Beck
    Pages 225-278

  11. Algebraic Combinations of Flows II

    • Anatole Beck
    Pages 279-314

  12. Fine Structure in \( {G_r}\left( \varphi \right) \)

    • Anatole Beck
    Pages 315-347

  13. Fine Structure in \({G_s}\left( {(\varphi } \right)){\text{I}}\)

    • Anatole Beck
    Pages 348-385

  14. Fine Structure in \({G_s}\left( {(\varphi } \right)){\text{I}}\)

    • Anatole Beck
    Pages 386-413

  15. Back Matter

    Pages 415-462
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Keywords

About this book

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 Dynaยญ 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.

Authors and Affiliations

  • University of Wisconsin, Madison, USA

    Anatole Beck

Bibliographic Information

  • Book Title: Continuous Flows in the Plane

  • Authors: Anatole Beck

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-65548-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin ยท Heidelberg 1974

  • Softcover ISBN: 978-3-642-65550-0Published: 28 January 2012

  • eBook ISBN: 978-3-642-65548-7Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 464

  • Topics: Topology

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