An overview of Caroline Series' 1985 symbolic dynamics model linking geodesic flows on the modular surface to continued fractions, including historical context and later developments.
Morse, A one-to-one representation of geodesics on a surface of negative curvature , Amer J Math 43 (1921) 33--51
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An elegant model of the geodesic flow on the modular surface
An overview of Caroline Series' 1985 symbolic dynamics model linking geodesic flows on the modular surface to continued fractions, including historical context and later developments.