**Memoirs of the American Mathematical Society**

2009;
106 pp;
Softcover

MSC: Primary 37;

Print ISBN: 978-0-8218-4427-4

Product Code: MEMO/201/945

List Price: $70.00

Individual Member Price: $42.00

**Electronic ISBN: 978-1-4704-0559-5
Product Code: MEMO/201/945.E**

List Price: $70.00

Individual Member Price: $42.00

# The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations

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*Tobias H. Jäger*

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

# Table of Contents

## The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations

- Contents v6 free
- Chapter 1. Introduction 18 free
- Chapter 2. Statement of the main results and applications 2128
- Chapter 3. Saddle-node bifurcations and sink-source-orbits 3643
- Chapter 4. The strategy for the construction of the sink-source-orbits 4451
- Chapter 5. Tools for the construction 5461
- Chapter 6. Construction of the sink-source orbits: One-sided forcing 7380
- Chapter 7. Construction of the sink-source-orbits: Symmetric forcing 9299
- Bibliography 105112