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Continued Fractions, Geodesic Flows and Ford Circles

In: Algorithms, Fractals, and Dynamics

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  • Hitoshi Nakada

    (Keio University, Department of Mathematics)

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.

Suggested Citation

  • Hitoshi Nakada, 1995. "Continued Fractions, Geodesic Flows and Ford Circles," Springer Books, in: Y. Takahashi (ed.), Algorithms, Fractals, and Dynamics, pages 179-191, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0321-3_16
    DOI: 10.1007/978-1-4613-0321-3_16
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