DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 809-818

Yuri Kifer

Title: Random Dynamics and its Applications

Random transformations emerge in a natural way as a model for description of a physical system whose evolution mechanism depends on time in a stationary way. This leads to the study of actions of compositions of different maps chosen from a typical sequence of transformations. The question whether such actions are chaotic can be dealt with employing the random thermodynamic formalism developped in recent years. This theory has nice applications to random networks, fractal dimensions of random sets and other models.

1991 Mathematics Subject Classification: Primary 58F11; Secondary 60J99, 60F15

Keywords and Phrases: random transformations, thermodynamic formalism, limit theorems

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