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June 2019 Bounds for Multiple Recurrence Rate and Dimension
Michihiro HIRAYAMA
Tokyo J. Math. 42(1): 239-253 (June 2019). DOI: 10.3836/tjm/1502179281

Abstract

We give an upper bound for the rate of simultaneous recurrence for some commuting family of measure preserving transformations. This provides a generalization of the Boshernitzan quantitative recurrence theorem for single transformation. We also give a lower bound for the Hausdorff dimension of the invariant measures for such transformations and for countable group actions.

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Michihiro HIRAYAMA. "Bounds for Multiple Recurrence Rate and Dimension." Tokyo J. Math. 42 (1) 239 - 253, June 2019. https://doi.org/10.3836/tjm/1502179281

Information

Published: June 2019
First available in Project Euclid: 18 July 2019

zbMATH: 07114908
MathSciNet: MR3982057
Digital Object Identifier: 10.3836/tjm/1502179281

Subjects:
Primary: 11B25
Secondary: 28A78, 37A15, 37A45

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

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Vol.42 • No. 1 • June 2019
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