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Multidimensional nonhyperbolic attractors

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Abstract

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.

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Authors and Affiliations

  1. IMPA, Est. D. Castorina 110 Jardim Botânico, 22460, Rio de Janeiro, Brazil

    Marcelo Viana

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  1. Marcelo Viana
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Partially supported by a J. S. Guggenheim Foundation Fellowship.

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Viana, M. Multidimensional nonhyperbolic attractors. Publications Mathématiques de l’Institut des Hautes Scientifiques 85, 63–96 (1997). https://doi.org/10.1007/BF02699535

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  • DOI: https://doi.org/10.1007/BF02699535

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