1. Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system.
- Author
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Heninger, Jeffrey M., Lippolis, Domenico, and Cvitanović, Predrag
- Subjects
- *
DISTRIBUTION (Probability theory) , *CHAOS theory , *STOCHASTIC processes , *APPROXIMATION theory , *DYNAMICAL systems , *STATE-space methods - Abstract
The finest state-space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation, the stochastic neighborhoods of deterministic periodic orbits can be computed from distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulas for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time expectation values of observables, can be expressed in this basis. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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