Topological analysis and synthesis of chaotic time series

We have developed a topological procedure for analyzing chaotic time series which identifies the stretching and squeezing mechanisms responsible for chaotic behavior in low-dimensional dynamical systems. These mechanisms, quantitatively described by a “template” or “knot-holder”, can then be used to...

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Bibliographic Details
Published in:Physica. D 1992-09, Vol.58 (1), p.229-242
Main Authors: Mindlin, Gabriel M., Gilmore, R.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Geometry, differential geometry, and topology
Mathematical methods in physics
Physics
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Summary:We have developed a topological procedure for analyzing chaotic time series which identifies the stretching and squeezing mechanisms responsible for chaotic behavior in low-dimensional dynamical systems. These mechanisms, quantitatively described by a “template” or “knot-holder”, can then be used to model the processes which generate the original chaotic data set.
ISSN:0167-2789
1872-8022
DOI:10.1016/0167-2789(92)90111-Y