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The backward continued fraction map and geodesic flow

Published online by Cambridge University Press:  19 September 2008

Roy L. Adler  and
Leopold Flatto
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
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 4 , December 1984 , pp. 487 - 492
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

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