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

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The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations is written by Tobias H. JŠger and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 082184427X (ISBN 10) and 9780821844274 (ISBN 13).

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'.