title: Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system.
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.
authors.affiliation: Department of Physics, University of Texas, Austin, Texas 78712, USA.
authors.forename: Jeffrey M
authors.initials: JM
authors.lastname: Heninger
authors.affiliation: Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
authors.forename: Domenico
authors.initials: D
authors.lastname: Lippolis
authors.affiliation: Center for Nonlinear Science and School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
authors.forename: Predrag
authors.initials: P
authors.lastname: Cvitanović