Ergodic theory of dynamical systems i.e., the qualitative analysis of iterations of a single transformation is nowadays a well developed theory. In 1945 S. Ulam and J. von Neumann in their short note 44] suggested to study ergodic theorems for the more general situation when one applies in turn different transforma- tions chosen at random. Their program was fulfilled by S. Kakutani 23] in 1951. 'Both papers considered the case of transformations with a common invariant measure. Recently Ohno 38] noticed that this condition was excessive. Ergodic theorems are just the beginning of ergodic...

Mathematicians often face the question to which extent mathematical models describe processes of the real world. These models are derived from experimental data, hence they describe real phenomena only approximately. Thus a mathematical approach must begin with choosing properties which are not very sensitive to small changes in the model, and so may be viewed as properties of the real process. In particular, this concerns real processes which can be described by means of ordinary differential equations. By this reason different notions of stability played an important role in the qualitative...