Asymptotics of Young diagrams and Hook numbers.
Ergodic Properties of the Erdös Measure, the Entropy of the Goldenshift, and Related Problems.
Geometry and dynamics of admissible metrics in measure spaces
We study a wide class of metrics in a Lebesgue space, namely the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the ɛ-entropy of a measure space with an admissible metric, etc. These notions and related results are applied to the theory of transformations with invariant measure; namely, we study the asymptotic properties of orbits in the cone of admissible metrics with respect to a given transformation...
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