On the definition of strange nonchaotic attractor

Volume 206 / 2009

Lluís Alsedà, Sara Costa Fundamenta Mathematicae 206 (2009), 23-39 MSC: Primary 37C55, 34D08, 37C70. DOI: 10.4064/fm206-0-2

Abstract

The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is “observable” in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove that a whole family of two-dimensional quasiperiodic skew products defined on ${\mathbb S}^1\times{\mathbb R}$ have strange nonchaotic attractors. As a corollary we show analytically that the system proposed by Grebogi et al. has a strange nonchaotic attractor.

Authors

  • Lluís AlsedàDepartament de Matemàtiques
    Edifici Cc
    Universitat Autònoma de Barcelona
    08913 Cerdanyola del Vallès, Barcelona, Spain
    e-mail
  • Sara CostaDepartament de Matemàtiques
    Edifici Cc
    Universitat Autònoma de Barcelona
    08913 Cerdanyola del Vallès, Barcelona, Spain
    e-mail

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