World Scientific Series on Nonlinear Science, Series A - Vol. 56

Strange nonchaotic attractors: dynamics between order and chaos in quasiperiodically forced systems


Ulrike Feudel,
Sergey Kuznetsov,
Arkady Pikovsky

 

This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed.

 

Contents:

1. Introduction
2. Models
3. Rational Approximations
4. Stability and Instability
5. Fractal and Statistical Properties
6. Bifurcations in Quasiperiodically Forced Systems and Transitions to SNA
7. Renormalization Group Approach to the Onset of SNA in Maps with the Golden-Mean Quasiperiodic Driving
8. Conclusion


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