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Published in:
2006 | OriginalPaper | Chapter
Beyond the Li-Yorke Definition of Chaos
Authors : Peter Kloeden, Zhong Li
Published in: Integration of Fuzzy Logic and Chaos Theory
Publisher: Springer Berlin Heidelberg
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Extensions of the well-known definition of chaos due to Li and Yorke for difference equations in ℝ
1
are reviewed for difference equations in ℝ
n
with either a snap-back repeller or saddle point as well as for mappings in Banach spaces and complete metric spaces. A further extension applicable to mappings in a space of fuzzy sets, namely the metric space (
ξ
n
,
D
) of fuzzy sets on the base space ℝ
n
, is then discussed and some illustrative examples are presented. The aim is to provide a theoretical foundation for further studies on the interaction between fuzzy logic and chaos theory.