# Scaling entropy and automorphisms with purely point spectrum ∗

@inproceedings{Birman2010ScalingEA,
title={Scaling entropy and automorphisms with purely point spectrum ∗},
author={M. Birman},
year={2010}
}
We study the dynamics of metrics generated by measure-preserving transformations. We consider sequences of average metrics and entropies of the measure with respect to these metrics. The main result, which gives a criterion for checking that the spectrum of a transformation if purely point, is that the scaling sequence for the -entropies with respect to the averages of an admissible metric is bounded if and only if the automorphism has a purely point spectrum. This paper is one of a series of… CONTINUE READING

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