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    Dajani, Karma Kraaikamp, Cor and van der Wekken, Niels 2013. Ergodicity of N-continued fraction expansions. Journal of Number Theory, Vol. 133, Issue. 9, p. 3183.

    Javaheri, Mohammad 2012. A Collatz-type conjecture on the set of rational numbers. Journal of Number Theory, Vol. 132, Issue. 11, p. 2582.

    IOMMI, GODOFREDO 2010. Multifractal analysis of the Lyapunov exponent for the backward continued fraction map. Ergodic Theory and Dynamical Systems, Vol. 30, Issue. 01, p. 211.

    Fan, Ai-Hua Wang, Bao-Wei and Wu, Jun 2007. Arithmetic and metric properties of Oppenheim continued fraction expansions. Journal of Number Theory, Vol. 127, Issue. 1, p. 64.

    Gröchenig, Karlheinz and Haas, Andrew 1996. Backward continued fractions, Hecke groups and invariant measures for transformations of the interval. Ergodic Theory and Dynamical Systems, Vol. 16, Issue. 06, p. 1241.

    Bogomolny, E.B. and Carioli, M. 1993. Quantum maps from transfer operators. Physica D: Nonlinear Phenomena, Vol. 67, Issue. 1-3, p. 88.

  • Ergodic Theory and Dynamical Systems, Volume 4, Issue 4
  • December 1984, pp. 487-492

The backward continued fraction map and geodesic flow

  • Roy L. Adler (a1) and Leopold Flatto (a2)
  • DOI:
  • Published online: 01 September 2008

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.

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[1]R. L. Adler & L. Flatto . 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.

[2]R. L. Adler & B. Weiss . The ergodic infinite measure preserving transformation of Boole. Israel J. of Math. 16 (1973), 263278.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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