Ergodic Theory and Dynamical Systems

Research Article

The backward continued fraction map and geodesic flow

Roy L. Adlera1 and Leopold Flattoa2

a1 IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA;

a2 Bell Laboratories, Murray Hill, New Jersey 07974, USA


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.

(Received August 01 1983)