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Structurally Unstable Quadratic Vector Fields of Codimension One

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

Table of contents

  1. Front Matter
    Pages i-vi
  2. Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 1-19
  3. Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 21-28
  4. Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 29-50
  5. Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 51-58
  6. Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 59-184
  7. Joan C. Artés, Jaume Llibre, Alex C. Rezende
    Pages 185-264
  8. Back Matter
    Pages 265-267

About this book

Introduction

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. 

Keywords

quadratic vector fields unstable codimension Poincaré quadratic systems structurally unstable of codimension one

Authors and affiliations

  • Joan C. Artés
    • 1
  • Jaume Llibre
    • 2
  • Alex C. Rezende
    • 3
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain
  3. 3.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-92117-4
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-92116-7
  • Online ISBN 978-3-319-92117-4
  • Buy this book on publisher's site