A Besicovitch cylindrical transformation  with Hölder function

Andrey Kochergin

doi:10.3934/era.2015.22.87

Article Contents

2015, Volume 22: 87-91. Doi: 10.3934/era.2015.22.87

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A Besicovitch cylindrical transformation with Hölder function

Andrey Kochergin^1,

1.
Lomonosov Moscow State University

Received: March 31, 2015

Revised: July 31, 2015

Published: January 2015

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Abstract

For any $\gamma\in(0,1)$ and any $\varepsilon>0$ we construct a cylindrical cascade over some irrational circle rotation with a $\gamma$-Hölder function such that the Besicovitch condition holds and the Hausdorff dimension of the set of points in the circle having discrete orbits is more than $1-\gamma-\varepsilon$. This result gives the answers to some questions of K. Frączek and M. Lemańczyk [1].

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Mathematics Subject Classification: 37B05, 37C45.

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References

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