Geodesic
Circle homeomorphisms and continued fractions
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 6, Tome 523 (2023), pp. 39-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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For an orientation preserving homeomorphism $f: \mathbb{T} \longrightarrow \mathbb{T}$ of the circle $\mathbb{T}=\mathbb{R}/ \mathbb{Z}$ with an irrational rotation number $\alpha_{f}$, we build karyon tilings $\mathcal{T}^{l}$ of levels $l=0,1,2,\ldots$ that are quasi-invariant with respect to $f$ and have minimal kernels. These tilings are used to obtain approximations for the rotation number $\alpha_{f}$ by continued fractions. 
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V. G. Zhuravlev. Circle homeomorphisms and continued fractions. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 6, Tome 523 (2023), pp. 39-52. http://geodesic.mathdoc.fr/item/ZNSL_2023_523_a3/

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