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Invariant measures for certain linear fractional transformations mod 1
Author(s):
Karlheinz
Gröchenig;
Andrew
Haas
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3439-3444.
MSC (1991):
Primary 11J70, 58F11, 58F03
Posted:
July 20, 1999
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Abstract:
Explicit invariant measures are derived for a family of finite-to-one, ergodic transformations of the unit interval having indifferent periodic orbits.
References:
- 1.
- R. L. Adler. Geodesic flows, interval maps and symbolic dynamics. In ``Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces'', T. Bedford, H. Keane, C. Series, eds., Oxford Univ. Press, 1991. CMP 92:02
- 2.
- A. F. Beardon, ``The Geometry of Discrete Groups'' Graduate Texts in Math. 91, Springer-Verlag, Berlin-Heidelberg-New York, 1987. MR 97d:22011
- 3.
- I. P, Cornfeld, S.V. Fomin and Ya. G. Sinai. Ergodic Theory, Springer-Verlag, Berlin-Heidelberg-New York, 1982. MR 87f:28019
- 4.
- K. Gröchenig and A. Haas, Backward continued fractions, invariant measures, and mappings of the interval. Ergodic Th. and Dyn. Sys. 16 (1996), 1241-1274. MR 97m:58114
- 5.
- W. de Melo and S. van Strien, One-Dimensional Dynamics, Ergebnisse d. Math. 25, Springer-Verlag, Berlin-Heidelberg-New York, 1993. MR 95a:58035
- 6.
- M. Thaler, Transformations on
![$[0,1]$](/proc/1999-127-12/S0002-9939-99-05008-X/gif-references/img254.gif) with infinite invariant measure. Israel J. Math. 46 (1983), 67-96. MR 85g:28020
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Additional Information:
Karlheinz
Gröchenig
Affiliation:
Department of Mathematics U-3009, The University of Connecticut, Storrs, Connecticut 06269-3009
Email:
groch@math.uconn.edu
Andrew
Haas
Affiliation:
Department of Mathematics U-3009, The University of Connecticut, Storrs, Connecticut 06269-3009
Email:
haas@math.uconn.edu
DOI:
10.1090/S0002-9939-99-05008-X
PII:
S 0002-9939(99)05008-X
Keywords:
Continued fractions,
interval maps,
invariant measures
Received by editor(s):
January 1, 1998
Posted:
July 20, 1999
Additional Notes:
The second author would like to thank the University of Washington for kindly providing access to their research facilities while this paper was in preparation.
Communicated by:
Linda Keen
Copyright of article:
Copyright
1999,
American Mathematical Society
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