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Series, Caroline

Non-euclidean geometry, continued fractions, and ergodic theory. (English) Zbl 0495.10032

Math. Intell. 4, 24-31 (1982).
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Cited in 9 Documents

MSC:

11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
28D05 Measure-preserving transformations
54H20 Topological dynamics (MSC2010)
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)

Keywords:

action of modular group on upper half plane; continued fractions; ergodicity of shift operator; ergodic behavior of geodesics; Riemann surface

Citations:

Zbl 0010.08403; JFM 51.0162.01
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Full Text: DOI

References:

[1] E. Artin, Ein mechanisches System mit quasi-ergodischen Bahnen, Collected Papers 499-501, Ed. Addison-Wesley, 1965
[2] G. H. Hardy and E. M. Wright, Theory of Numbers, Oxford University Press · Zbl 0020.29201
[3] Hedlund, G. A., A metrically transitive group defined by the modular group, Amer. J. Math, 57, 668-678 (1935) · JFM 61.1108.04 · doi:10.2307/2371195
[4] E., Hopf, Ergodentheorie, Ber. Verh. Sachs, Akad. Wiss. Leipzig, 91, 261-261 (1939)
[5] A., Ya, Khinchin, Metrische Kettenbruchprobleme, Compositio Math, 1, 361-382 (1935) · Zbl 0010.34101
[6] C., Series, The infinite word problem and Fuchsian groups, J. Ergodic Theory and Dynamical Systems, 1, 337-360 (1981) · Zbl 0488.05039
[7] C. Series, On Coding Geodesies with Continued Fractions, Monographie 29, ĽEnseignement Mathématique, Univ. de Genève, 1981 · Zbl 0476.58018
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