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Chaos and quasiperiodicity in diffeomorphisms of the solid torus
1.  Dept. of Mathematics, University of Groningen, Blauwborgje 3, 9747 AC Groningen, Netherlands 
2.  Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona 
3.  College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, North Park Road, EX4 4QF, Exeter 
This type of attractor is here investigated in a model map of the solid torus, constructed by a skew coupling of the Hénon family of planar maps with the Arnol$'$d family of circle maps. It is proved that Hénonlike strange attractors occur in certain parameter domains. Numerical evidence is produced, suggesting that quasiperiodic circle attractors and quasiperiodic Hénonlike attractors persist in relatively large subsets of the parameter space. We also discuss two problems in the numerical identification of socalled strange nonchaotic attractors and the persistence of all these classes of attractors under perturbation of the skew product structure.
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