Progress in the analysis of experimental chaos through periodic orbits
- Paul Scherrer Institute, CH-5232 Villigen (Switzerland)
- Physics Institute, University of Zuerich, CH-8057 Zuerich (Switzerland)
The understanding of chaotic systems can be considerably improved with the knowledge of their periodic-orbit structure. The identification of the low-order unstable periodic orbits embedded in a strange attractor induces a hierarchical organization of the dynamics which is invariant under smooth coordinate changes. The applicability of this technique is by no means limited to analytical or numerical calculations, but has been recently extended to experimental time series. As a specific example, the authors review some of the major results obtained on a nuclear-magnetic-resonance laser which have led to an extension of the conventional (Bloch-Kirchhoff) equations of motion, to the construction of approximate generating partitions, and to an efficient control of the chaotic system around various unstable periodic orbits. The determination of the symbolic dynamics, with the precision achieved by recording all unstable cycles up to order 9, improves the topological and metric characterization of a heteroclinic crisis. The periodic-orbit approach permits detailed study of chaotic motion, thereby leading to an improved classification scheme which subsumes the older ones, based on estimates of scalar quantities such as fractal dimensions and metric entropies.
- OSTI ID:
- 6644894
- Journal Information:
- Reviews of Modern Physics; (United States), Vol. 66:4; ISSN 0034-6861
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
DYNAMICS
ORBITS
BLOCH EQUATIONS
ENTROPY
FRACTALS
LASER RADIATION
PHASE SPACE
ELECTROMAGNETIC RADIATION
EQUATIONS
MATHEMATICAL SPACE
MECHANICS
PHYSICAL PROPERTIES
RADIATIONS
SPACE
THERMODYNAMIC PROPERTIES
661300* - Other Aspects of Physical Science- (1992-)