Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system

Autor:	Heninger, Jeffrey M., Lippolis, Domenico, Cvitanovic, Predrag
Rok vydání:	2015
Předmět:	Nonlinear Sciences - Chaotic Dynamics
Zdroj:	Phys. Rev. E 92, 062922 (2015)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevE.92.062922
Popis:	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. Comment: 6 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1507.00462 Zobrazit plný text záznamu View this record from Arxiv