The paper addresses the theory of strange attractors and their bifurcations. All known attractors can be divided into three types: hyperbolic and pseudo-hyperbolic attractors as well as quasi-attractors. The Anosov and Smale-Williams attractors are examples of hyperbolic ones and they can be born by some global bifurcations. For attractors of the second type, we give a definition and describe their main properties. Lorenz-like and spiral attractors belong to this type. They are structurally unstable, moreover, spiral attractors allow homoclinic tangencies but their perturbations do not lead to the appearance of stable periodic motions. Otherwise, quasi-attractors allow the existence of stable periodic orbits of large periods and with narrow attracting domains. The latter attractors are often met in problems of nonlinear dynamics of systems with a complicated orbit behavior.
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