Title: A Case of Anything Goes in Infinite Ergodic Theory

Speaker: Terry Adams, US DoD

Seminar Type: Ergodic Theory/Probability

Abstract: Dynamical systems are well studied in the finite measure preserving case. Many of the same principles do not apply for infinite measure preserving transformations. As an example, for an invertible finite measure preserving transformation, its Cartesian product is ergodic if and only if it is weak mixing. As a consequence, all products of all non-zero powers are ergodic. In the case of invertible infinite measure preserving transformations, the situation is quite different. We give a class of transformations that demonstrate just about any reasonable behavior when it comes to ergodicity and conservativity of products of powers. Also, we’ll provide background on “weak” mixing notions in infinite measure.