1993/02/03 by Nicholas Tufillaro, Nicholas B. Tufillaro, Tufillaro, Nicholas B.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Mathematical Dynamics and Fractals #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9302001
CYCLER Paper 93feb001 LaTeX with natokap.sty and nato11.sty macros (available via `get nato.sty')
arxiv created 1993/02/03 · openalex publication_date 1993/02/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.