Donald Samuel Ornstein

Donald Samuel Ornstein ( born July 30, 1934 in New York) is an American mathematician who works in the field of ergodic theory.

Ornstein in 1957 his doctorate at the University of Chicago under the direction of Irving Kaplansky. During his career at Stanford University, he supervised the doctoral thesis of twenty-three students.

He achieved fame in 1968 through his work on the isomorphism of Bernoulli pictures ( Bernoulli shifts), for which he was awarded the 1974 Bôcher Memorial Prize. Bernoulli pictures are stochastic processes generalize the shifts in the space of sequences of coin tosses. In each time step, a value i is accepted from a supply of N values ​​with probability. Ornstein proved the equivalence ( in terms of their stochastic behavior ) of Bernoulli shifts by if its Kolmogorov entropy defined, is the same. The equivalence is defined by maßerhaltende isomorphisms ( one-one pictures the state spaces ) for which the Kolmogorov entropy is an invariant, as Andrei Kolmogorov and Yakov Sinai in 1958 showed. Bernoulli shifts are therefore by Kolmogorov and Sinai not all equivalent to one another, as Ornstein showed however, they are equivalent if the entropy is the same.

Since 1981 he is a member of the National Academy of Sciences. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Entropy is enough to classify Bernoulli shifts but not K- automorphisms ). He is a Fellow of the American Mathematical Society.

Writings

• Ergodic theory, randomness, and dynamical systems, Yale University Press, 1974
• Ornstein Ornstein isomorphism theorem