Geodesic
Besicovitch Cylindrical Transformation with a~H\"older Function
Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 366-375

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For any $\gamma\in(0,1)$ and $\varepsilon>0$, we construct a cylindrical cascade with a $\gamma$-Hölder function over some rotation of the circle. This transformation has the Besicovitch property; i.e., it is topologically transitive and has discrete orbits. The Hausdorff dimension of the set of points of the circle that have discrete orbits is greater than $1-\gamma-\varepsilon$.
Keywords: cylindrical transformation, Besicovitch property, Hölder property
Mots-clés : Hausdorff dimension. 
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     author = {A. V. Kochergin},
     title = {Besicovitch {Cylindrical} {Transformation} with {a~H\"older} {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {366--375},
     publisher = {mathdoc},
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     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a5/}
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A. V. Kochergin. Besicovitch Cylindrical Transformation with a~H\"older Function. Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 366-375. http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a5/