Michael Keane (Wesleyan U.)

will speak on

Ergodicity of some adic transformations

Abstract:

There has been quite a bit of interest recently in a special adic transformation which I call the binomial transformation - it also goes by the name of Pascal. After explaining the definition and elementary properties, I shall give two proofs of the ergodicity of this transformation. One of the proofs exhibits all ergodic invariant measures associated with the transformation, and the other can be generalized to give a proof of the ergodicity of the Euler transformation, another adic transformation which was previously not known to be ergodic. The invariant measure structure of the Euler transformation is still unknown, and it is also not known whether any of these transformations satisfy nice spectral properties, such as weak or strong mixing. The method is widely applicable to other adic transformations.

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Last update on 20/10/02.