ABOUT SEVERAL PROBLEMS OF MATHEMATICAL-TH EORY OF CLIMATE

The problem of construction of an invariant measure concentrated on an attractor of a climatic system is one of central problems of mathemat ical theory of climate. The paper presents main theorems which answer the principal question on existence and uniqueness of such a measure. Unfortunately, there is no constructive algorithm to construct it nowa days. We consider a special case when the measure is concentrated in t he neighborhoods of stationary points, i.e., the climatic system behav es so that mostly it stays in the vicinity of these points. In the cas e of two stationary points we observe two quasistationary regimes of c irculation. The theoretical results were applied to the analysis of ci rculation over the region of north Atlantic generated by the model of general circulation of the atmosphere developed in the Institute of Nu merical Mathematics of Russian Academy of Sciences. Isolated circulati on regimes are close to well known regimes of the type of zonal flow a nd blocking.