Topological organization of (low-dimensional) chaos
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 &ny 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.
- Research Organization:
- Los Alamos National Lab., NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 10110821
- Report Number(s):
- LA-UR-92-3235; CONF-9208188-1; ON: DE93003693
- Resource Relation:
- Conference: North Atlantic Treaty Organization/Advanced Studies Institute (NATO/ASI) summer school: from statistical physics to statistical inference and back,Cargese (France),31 Aug - 12 Sep 1992; Other Information: PBD: [1992]
- Country of Publication:
- United States
- Language:
- English
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