Backward continued fractions and their invariant measures

Canadian Mathematical Bulletin

Volumn 39, Issue 2, 1996, Pages 186-198

  Gröchenig, Karlheinz ^a   Haas, Andrew ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Continued fractions; Interval maps; Invariant measures; Symbolic dynamics

Indexed keywords

EID: 0030167130     PISSN: 00084395     EISSN: None     Source Type: Journal    
DOI: 10.4153/CMB-1996-023-8     Document Type: Article

References (14)

1. R. L. Adler and L. Flatto, Cross-section maps for geodesic flows. In: Ergodic Theory and Dynamical Systems, Progress in Math. 2, (ed. A. Katok), Birkhäuser, Boston, 1980.
2. _, The backward continued fraction map and the geodesic flow, Ergodic Theory Dynamical Systems 4(1984), 487-492.
3. _, Geodesic flows, interval maps, and symbolic dynamics, Bull. Amer. Math. Soc. 25(1991), 229-334.
4. K. Gröchenig and A. Haas, Backward continued fractions, Hecke groups and invariant measures for transformations of the interval, Ergodic Theory Dynamical Systems, to appear.
5. F. Hofbauer, On the intrinsic ergodicity of piecewise monotonic transformations with positive entropy, Israel J. Math. 34(1979), 213-237.
6. _, The structure of piecewise monotonic transformations, Ergodic Theory Dynamical Systems 1(1981), 159-178.
7. W. de Melo and S. van Strien, One-Dimensional Dynamics, Ergebnisse d. Math. Vol. 25, Springer, Berlin, Heidelberg, 1993.
8. A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Hungary 8(1957), 477-493.
9. _, Valòs szàmok elöàllitàsàra szölgàlò algoritmusokròl, M. T. A. Mat. Oszt. Kz̈l. 7(1957), 265-293.
10. M. Rychlik, Bounded variation and invariant measures, Studia Math. 76(1983), 69-80.
11. R. Salem, On some singular monotonie functions which are strictly increasing, Trans. Amer. Math. Soc. 53(1943), 427-439.
12. F. Schweiger, Invariant measures of generalized Renyi maps, Univ. Salzburg, 1993, preprint.
13. C. Series, The modular group and continued fractions, J. London Math. Soc. 31(1985), 69-80.
14. M. Thaler, Transformations on [0, 1] with infinite invariant measure, Israel J. Math. 46(1983), 67-96.