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Statistical properties of 2-D generalized hyperbolic attractors
V. S. Afraimovich1, N. I. Chernov, E. A. Sataev
1Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia 30332Institute of Nuclear Power Engineering, Obninsk 249020, Studgorodok, Russia.
Chaos (Woodbury, N.Y.)
|March 1, 1995
Summary
This study establishes a stretched exponential bound on correlation decay and a central limit theorem for hyperbolic attractors. It also identifies conditions for applying these results to Belykh and Lozi attractors.
Area of Science:
- Dynamical Systems and Chaos Theory
- Statistical Physics
Background:
- Pesin's work introduced hyperbolic attractors and the Smale spectral decomposition.
- Understanding the statistical properties of dynamical systems is crucial.
Purpose of the Study:
- To establish a stretched exponential bound on the decay of correlations for hyperbolic attractors.
- To prove the central limit theorem for these systems.
- To investigate the applicability of these results to specific attractors like Belykh and Lozi.
Main Methods:
- Utilizing techniques related to hyperbolic attractors and spectral decomposition.
- Applying methods for analyzing correlation functions in dynamical systems.
- Developing criteria for attractor classification.
Main Results:
- A stretched exponential bound on the decay of correlations was established.
- The central limit theorem was proven for the considered class of hyperbolic attractors.
- Conditions were identified for the Belykh and Lozi attractors to satisfy the main results.
Conclusions:
- The findings provide significant insights into the statistical behavior of hyperbolic attractors.
- The results generalize previous work and extend to specific, notable attractors.
- This research contributes to a deeper understanding of chaotic dynamical systems.