Universal strange attractors on wrinkled tori

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Abstract
Strange attractors in dynamical systems that go to chaos via quasiperiodicity are considered. It is shown that there exists an infinite number of points in parameter space where the topology of the strange attractors is universal. At such points the periodic points belonging to unstable periodic orbits can be organised on ternary trees which are pruned by local rules. The grammar is universal, and thus the topological entropy is universal at each of these points in parameter space. The complete understanding of the topology is used to calculate systematically the metric properties of the attractors. The spectrum of scaling indices f( alpha ) is computed. It is found that there is no metric universality, although some aspects of the metric properties are universal. Experiments to test some of the predictions of this theory are suggested.