Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system
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 neighborhoods of deterministic periodic orbits can be computed as distributions stationary under the action of a local Fokker-Planck operator...
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| creator | Heninger, Jeffrey M Lippolis, Domenico Cvitanovic, Predrag |
| description | 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 neighborhoods of deterministic periodic orbits can be computed as distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulae 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. |
| doi_str_mv | 10.48550/arxiv.1507.00462 |
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| source | Freely Accessible Journals; arXiv.org |
| subjects | Chaos theory Markov analysis Mathematical analysis Neighborhoods Operators (mathematics) Orbits Physics - Chaotic Dynamics |
| title | Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system |
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