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Multidimensional nonhyperbolic attractors. (English) Zbl 1037.37016
Summary: We construct smooth transformations and diffeomorphisms exhibiting nonuniformly hyperbolic attractors with multidimensional sensitiveness on initial conditions: typical orbits in the basin of attraction have several expanding directions. These systems also illustrate a new robust mechanism of sensitive dynamics: despite the nonuniform character of the expansion, the attractor persists in a full neighbourhood of the initial map.

##### MSC:
 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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