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Observation of structure in the Lorenz map
1Departamento de Fisica, Universidad de Los Andes, A.A. 4976, Bogota, Colombia.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
Researchers numerically integrated the Lorenz system to reveal structure in its Poincare map. The study estimates the capacity dimension, aligning with prior correlation dimension measurements of the Lorenz attractor.
Area of Science:
- * Dynamical Systems and Chaos Theory
- * Nonlinear Dynamics
Background:
- * The Lorenz system is a simplified mathematical model that exhibits chaotic behavior.
- * Understanding the geometric and dimensional properties of attractors is crucial in chaos theory.
Purpose of the Study:
- * To investigate the structure of the Poincare map for the Lorenz system.
- * To estimate the capacity dimension of the Lorenz attractor.
Main Methods:
- * Extensive numerical integration of the Lorenz system equations.
- * Analysis of the resulting phase space trajectories to construct the Poincare map.
- * Calculation of the capacity dimension from the observed attractor structure.
Main Results:
- * Discernible structure was identified within the Poincare map of the Lorenz system.
- * The estimated capacity dimension of the Lorenz attractor was found to be consistent with previous correlation dimension measurements.
Conclusions:
- * Numerical integration provides insights into the complex structure of the Lorenz attractor.
- * Capacity dimension estimation offers a valid method for characterizing the fractal nature of chaotic attractors.