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Symmetry properties of periodic orbits extracted from scattering data
O Merlo1, C Jung, T H Seligman
1Institut für theoretische Physik, Universität Basel, Switzerland.
Chaos (Woodbury, N.Y.)
|December 1, 2004
Summary
This study reveals how to extract discrete system symmetries from scattering data. The method simultaneously identifies periodic orbits, Lyapunov exponents, and symmetry breaking effects.
Area of Science:
- Physics
- Dynamical Systems
- Chaos Theory
Background:
- Discrete symmetries govern system properties, particularly periodic orbits.
- Extracting these symmetries from experimental data is challenging.
- Fractal structures in scattering functions contain hidden symmetry information.
Purpose of the Study:
- To develop a method for extracting discrete system symmetries from scattering data.
- To simultaneously determine periodic orbits and Lyapunov exponents alongside symmetries.
- To analyze the impact of symmetry breaking on scattering data.
Main Methods:
- Utilizing a recent method to analyze the scaling of fractal structures in scattering functions.
- Applying this method to extract information from scattering data.
- Investigating the effects of small symmetry-breaking perturbations.
Main Results:
- Demonstrated successful extraction of discrete symmetries from scattering data.
- Showcased simultaneous determination of periods and Lyapunov exponents.
- Quantified the changes in scattering data due to symmetry breaking.
Conclusions:
- The developed method effectively extracts discrete symmetries from scattering data.
- This approach provides simultaneous insights into periodic orbits, Lyapunov exponents, and symmetry breaking.
- Offers a novel way to probe system symmetries using scattering experiments.
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