On the definition of strange nonchaotic attractor

Lluís Alsedà, and Sara Costa. "On the definition of strange nonchaotic attractor." Fundamenta Mathematicae 206.1 (2009): 23-39. <http://eudml.org/doc/282942>.

@article{LluísAlsedà2009,
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 𝕊¹ × ℝ have strange nonchaotic attractors. As a corollary we show analytically that the system proposed by Grebogi et al. has a strange nonchaotic attractor.},
author = {Lluís Alsedà, Sara Costa},
journal = {Fundamenta Mathematicae},
keywords = {quasiperiodically forced system; strange nonchaotic attractor; Lyapunov exponents},
language = {eng},
number = {1},
pages = {23-39},
title = {On the definition of strange nonchaotic attractor},
url = {http://eudml.org/doc/282942},
volume = {206},
year = {2009},
}

TY - JOUR
AU - Lluís Alsedà
AU - Sara Costa
TI - On the definition of strange nonchaotic attractor
JO - Fundamenta Mathematicae
PY - 2009
VL - 206
IS - 1
SP - 23
EP - 39
AB - 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 𝕊¹ × ℝ have strange nonchaotic attractors. As a corollary we show analytically that the system proposed by Grebogi et al. has a strange nonchaotic attractor.
LA - eng
KW - quasiperiodically forced system; strange nonchaotic attractor; Lyapunov exponents
UR - http://eudml.org/doc/282942
ER -