Skip to Main Content


AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution


The $2$-dimensional attractor of $x’(t)=-𝜇x(t)+f(x(t-1))$

About this Title

Hans-Otto Walther

Publication: Memoirs of the American Mathematical Society
Publication Year: 1995; Volume 113, Number 544
ISBNs: 978-0-8218-2602-7 (print); 978-1-4704-0123-8 (online)
DOI: https://doi.org/10.1090/memo/0544
MathSciNet review: 1230775
MSC: Primary 58F32; Secondary 34K15, 39B12, 58F12

PDF View full volume as PDF

Read more about this volume

View other years and numbers:

Table of Contents

Chapters

  • 1. Introduction
  • 2. Notation, preliminaries
  • 3. Basic properties of solutions
  • 4. Attractors
  • 5. Phase space decomposition
  • 6. A-priori estimates, phase curves with trivial $\alpha$-limit set, and invariant manifolds
  • 7. Graph representation
  • 8. Transversals
  • 9. Angles along projected phase curves
  • 10. The Poincaré-Bendixson Theorem
  • 11. Proof of Theorem 7.1(ii)