Mathematical Sciences: Topics in Ergodic Theory and Dynamical Systems

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Professor Feldman will continue his research in ergodic theory giving particular attention to the following areas: (i) normal distributions with respect to p,q multiplication, (ii) continuous products of probability spaces, (iii) ergodic theory for actions of amenable (non-unimodular) groups, (iv) smooth ergodic theory, and (v) subrelations of ergodic equivalence relations. Research in ergodic theory involves trying to understand the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. Another important theme in ergodic theory is the classification of systems into broad categories which are mathematically identical in an abstract sense. Professor Feldman's research will make contact with these areas.