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Chaotic and strange attractors of a two-dimensional map

A family of continuous, invertible standard maps of the torus, cylinder and plane is considered in this paper. Sequences of bifurcations are studied which correspond to the transformation of an invariant curve to chaotic and strange attractors. The characteristic variations of complicated attractors are considered. Hyperbolicity conditions are obtained for the case of piecewise-smooth maps. The maps generating the Henon, Lozi, Belykh attractors belong to our class of standard maps.