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The backward continued fraction map and geodesic flow

Published online by Cambridge University Press:  19 September 2008

Roy L. Adler
Affiliation:
IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA;
Leopold Flatto
Affiliation:
Bell Laboratories, Murray Hill, New Jersey 07974, USA
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Abstract

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The ‘backward continued fraction’ map studied by A. Reyni is defined by y = g(x) where g(x) equals the fractional part of 1/(1−x) for 0 < x < 1. We show that it is a factor map of a special cross-section map for the geodesic flow on the unit tangent bundle of the modular surface. This gives an alternative derivation of the fact that this map preserves the infinite measure dx/x on the unit interval.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Adler, R. L. & Flatto, L.. Cross section map for the geodesic flow on the modular surface. In Conference in Modern Analysis and Probability (Contemporary Math. 26 (1984), 924). Amer. Math. Soc: Providence, R. I.CrossRefGoogle Scholar
[2]Adler, R. L. & Weiss, B.. The ergodic infinite measure preserving transformation of Boole. Israel J. of Math. 16 (1973), 263278.CrossRefGoogle Scholar
[3]Billingsley, P.. Ergodic Theory and Information. John Wiley Sons, Inc.: New York (1965).Google Scholar
[4]Nitecki, Z.. Topological dynamics on the interval. In Ergodic Theory and Dynamical Systems, (Proc. Special Year Md. 1979–1980) Progress in Math., vol. 2, 173. Birkhauser: Boston, Basel & Stuttgart.Google Scholar
[5]Renyi, A.. Valós számok elöállitására szölgáló algoritmusokról. M.T.A. Mat. és Fiz. Oszt. Közl. 7 (1957), 265293.Google Scholar