Abstract
A purpose of this paper is to give a short sketch of a relation between continued fractions and the hyperbolic geometry on the upper half plane, (the simple continued fractions case and a generalized case). Relations between continued fractions and the geodesic flows on the modular surface are well-known. For example, Adler and Flatto [1] showed that the continued fraction transformation is obtained as a cross-section map of the geodesic flow. Another interesting one is due to Moeckel [8], who proved a metrical property of continued fractions concerning to a distribution of digits by using the Farey tessellation and the ergodicity of geodesic flows.
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References
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© 1995 Plenum Press, New York
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Nakada, H. (1995). Continued Fractions, Geodesic Flows and Ford Circles. In: Takahashi, Y. (eds) Algorithms, Fractals, and Dynamics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0321-3_16
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DOI: https://doi.org/10.1007/978-1-4613-0321-3_16
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