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Geometry of repeated measurements in chaotic systems
1Natural Sciences Division, University of Hawaii, Hilo, Hawaii 96720-4091, USA. pbinder@hawaii.edu
Chaos (Woodbury, N.Y.)
|April 8, 2010
Summary
This study introduces joint probability matrices to analyze chaotic systems. These matrices reveal topological and metric information, aiding in understanding system dynamics and information decay.
Area of Science:
- Dynamical Systems
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Chaotic systems are complex and challenging to analyze.
- Understanding the evolution of information within these systems is crucial.
Purpose of the Study:
- To develop a method using joint probability matrices for analyzing chaotic systems.
- To investigate the information decay in chaotic systems.
- To reconstruct attractors of chaotic systems.
Main Methods:
- Utilizing joint probability matrices derived from coarse-grained measurements.
- Constructing transfer matrices for one-dimensional piecewise linear maps.
- Directly generating matrices from numerical data for 3D continuous-time systems.
Main Results:
- Joint probability matrices capture both topological and metric properties.
- Mutual information decay is linked to the eigenvalues of transfer matrices.
- Generated matrices provide attractor reconstructions with probability measure information.
Conclusions:
- Joint probability matrices offer a powerful tool for characterizing chaotic systems.
- The method is applicable to both discrete and continuous chaotic systems.
- This approach enhances the understanding of information dynamics and attractor properties.
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