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Convex delay endomorphisms

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Abstract

In this paper delay equationsx n+k =f(x n ,...,x n+k−1) are considered, where the functionf is supposed to be convex, having a unique point of maximum. It is proved that if there are no stationary solutions then all solutions must diverge. Considering the one parameter familyf μ=μ+f and associating to it a family of two dimensional mapsF μ it is shown that the set of points having bounded orbit underF μ is homeomorphic to the product of a Cantor set and a circle, and is hyperbolic and stable.

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Authors and Affiliations

  1. Centro de Matemática, Universidad de la República, Ed. Acevedo 1139, 11200, Montevideo, Uruguay

    A. Rovella

  2. IMERL-Facultad de Ingeniería, Universidad de la República CC 30, 11200, Montevideo, Uruguay

    A. Rovella

  3. Departament de Matemática Aplicada 2, Escola Tecnica Superior d'Enginyers Industrials, Colom 11, 08222, Terrassa, Barcelona, Espanya

    F. Vilamajó

Authors
  1. A. Rovella
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  2. F. Vilamajó
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Communicated by A. Jaffe

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Rovella, A., Vilamajó, F. Convex delay endomorphisms. Commun.Math. Phys. 174, 393–407 (1995). https://doi.org/10.1007/BF02099608

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  • DOI: https://doi.org/10.1007/BF02099608

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