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The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations
Tobias H. Jäger, Universität Erlangen-Nürnberg, Germany
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Memoirs of the American Mathematical Society
2009; 106 pp; softcover
Volume: 201
ISBN-10: 0-8218-4427-X
ISBN-13: 978-0-8218-4427-4
List Price: US$66
Individual Members: US$39.60
Institutional Members: US$52.80
Order Code: MEMO/201/945
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The author proposes a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddle-node bifurcation, but instead of a neutral invariant curve there exists a strange non-chaotic attractor-repeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls `exponential evolution of peaks'.

Table of Contents

  • Introduction
  • Statement of the main results and applications
  • Saddle-node bifurcations and sink-source-orbits
  • The strategy for the construction of the sink-source-orbits
  • Tools for the construction
  • Construction of the sink-source orbits: One-sided forcing
  • Construction of the sink-source-orbits: Symmetric forcing
  • Bibliography
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