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