Statistical Characteristics of Barotropic Atmospeheric System and Its Unstable Periodic Solutions

This paper is devoted to the problem of approximating an invariant measure and statistical characteristics of barotropic atmospheric model with the help of its periodic trajectories. In this procedure orbits are taken into account according to their weights defined by the orbit instability characteristics. The method comes from the dynamical systems theory where in several specific case (for hyperbolic systems in particular) unstable periodic orbits define the system invariant measure. In our study we show that the system PDF could be reconstructed with the error less than 10% provided that the optimal orbit weight function is chosen.