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  • © 2018

Structurally Unstable Quadratic Vector Fields of Codimension One

Birkhäuser
  • Follows a similar work on structurally stable systems

  • Proves that there are at most 211 and at least 204 structurally unstable codimension one topologically different phase portraits in the Poincaré disc modulo limit cycles

  • Gives an overview on recent research in the area

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-vi
  2. Introduction

    • Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 1-19
  3. Preliminary Definitions

    • Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 21-28
  4. Some Preliminary Tools

    • Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 29-50
  5. A Summary of Structurally Stable Quadratic Vector Fields

    • Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 51-58
  6. Proof of Theorem 1.1(a)

    • Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 59-184
  7. Proof of Theorem 1.1(b)

    • Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 185-264
  8. Back Matter

    Pages 265-267

About this book

Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors’ work on structurally stable planar quadratic polynomial differential systems. In the present work the authors aim at finding all possible phase portraits in the Poincaré disc, modulo limit cycles, of planar quadratic polynomial differential systems manifesting the simplest level of structural instability. They prove that there are at most 211 and at least 204 of them. 

Authors and Affiliations

  • Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain

    Joan C. Artés, Jaume Llibre, Alex C. Rezende

Bibliographic Information

  • Book Title: Structurally Unstable Quadratic Vector Fields of Codimension One

  • Authors: Joan C. Artés, Jaume Llibre, Alex C. Rezende

  • DOI: https://doi.org/10.1007/978-3-319-92117-4

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Softcover ISBN: 978-3-319-92116-7Published: 06 July 2018

  • eBook ISBN: 978-3-319-92117-4Published: 28 June 2018

  • Edition Number: 1

  • Number of Pages: VI, 267

  • Number of Illustrations: 361 b/w illustrations, 1 illustrations in colour

  • Topics: Ordinary Differential Equations, Dynamical Systems and Ergodic Theory

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access