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- W2951706889 abstract "We study a wide class of metrics in a Lebesgue space with a standard measure, 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 -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 or a group of transformations. The main result of this paper is a new discreteness criterion for the spectrum of an ergodic transformation: we prove that the spectrum is discrete if and only if the -entropy of the averages of some (and hence any) admissible metric over fragments of its trajectory is uniformly bounded." @default.
- W2951706889 created "2019-06-27" @default.
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- W2951706889 date "2012-05-06" @default.
- W2951706889 modified "2023-09-26" @default.
- W2951706889 title "Geometry and Dynamics of Admissible Metrics in Measure Spaces" @default.
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