Topological organization of (low-dimensional) chaos

Details Topological organization of (low-dimensional) chaos Topological organization of (low-dimensional) chaos

1993-02-03

arxiv.org/abs/chao-dyn/9302001v1

Nonlinear Sciences

Chaotic Dynamics

CYCLER Paper 93feb001 LaTeX with natokap.sty and nato11.sty macros (available via `get nato.sty')

Scientific paper

Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with any model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series.

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