Unstable periodic trajectories of a barotropic model of the atmosphere

Abstract

Unstable periodic trajectories of a chaotic dissipative system belong to the attractor of the system and are its important characteristics. Many chaotic systems have an infinite number of periodic solutions forming the skeleton of the system attractor. This allows one to approximate the system trajectories and statistical characteristics by using periodic solutions. The least unstable orbits may generate local maxima of the system state distribution functions on the attractor. With respect to atmospheric systems this means that orbits may determine dynamic circulation regimes and typical variability modes of the system. In some cases, given a small number of periodic solutions, one can describe the dynamics on the attractor of the system and the basic statistics with sufficient precision. Thus, the information concerning periodic trajectories of a particular dynamic system may be very important for analysis of its behavior.