# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## On the definition of strange nonchaotic attractor

### Tom 206 / 2009

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

#### Streszczenie

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.

#### Autorzy

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