Markov maps associated with fuchsian groups

Rufus Bowen; Caroline Series

Publications Mathématiques de l'IHÉS (1979)

  • Volume: 50, page 153-170
  • ISSN: 0073-8301

How to cite


Bowen, Rufus, and Series, Caroline. "Markov maps associated with fuchsian groups." Publications Mathématiques de l'IHÉS 50 (1979): 153-170. <>.

author = {Bowen, Rufus, Series, Caroline},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {Fuchsian groups; Markov maps},
language = {eng},
pages = {153-170},
publisher = {Institut des Hautes Études Scientifiques},
title = {Markov maps associated with fuchsian groups},
url = {},
volume = {50},
year = {1979},

AU - Bowen, Rufus
AU - Series, Caroline
TI - Markov maps associated with fuchsian groups
JO - Publications Mathématiques de l'IHÉS
PY - 1979
PB - Institut des Hautes Études Scientifiques
VL - 50
SP - 153
EP - 170
LA - eng
KW - Fuchsian groups; Markov maps
UR -
ER -


  1. [1] R. ADLER, Continued fractions and Bernoulli Trials, Ergodic Theory Lecture Notes, J. Moser, E. Phillips, S. Varadhan, Courant Institute, N.Y.U., 1975. 
  2. [2] E. ARTIN, Ein mechanisches System mit quasiergodischen Bahnen, Collected Papers, Addison Wesley, 1965, p. 499-501. 
  3. [3] L. BERS, Uniformization, moduli and Kleinian groups, Bull. London Math. Soc., 4 (1972), 257-300. Zbl0257.32012MR50 #595
  4. [3 a] L. BERS, On Hilbert's 22nd problem, Proc. Symp. Pure Math., 28 (1976), 559-609. Zbl0348.30013MR55 #654
  5. [4] R. BOWEN, Anosov foliations are hyperfinite, Ann. Math., 106 (1977), 549-565. Zbl0374.58008MR57 #1569
  6. [5] R. BOWEN, Invariant measures for Markov maps of the interval, Comm. Math. Phys. (1979). Zbl0421.28016MR81e:28010
  7. [6] R. BOWEN, Hausdorff dimension of quasi-circles, Publ. Math. I.H.E.S., 50 (1979). Zbl0439.30032MR81g:57023
  8. [7] L. R. FORD, Automorphic Functions, New York, McGraw-Hill, 1929 (1st edition). JFM55.0810.04
  9. [8] G. A. HEDLUND, A metrically transitive group defined by the modular group, Amer. J. Math., 57 (1935), 668-678. Zbl0012.20301JFM61.1108.04
  10. [9] G. A. HEDLUND, On the metrical transitivity of the geodesics on closed surfaces of constant negative curvature, Ann. Math., 35 (1934), 787-808. Zbl0010.22107JFM60.0614.02
  11. [10] T. KUUSALO, Boundary mappings of geometric isomorphisms of Fuchsian groups, Ann. Acad. Sci. Fennicae, Ser A. Math., 545, 1973, 1-7. Zbl0272.30023MR49 #7437
  12. [11] B. MASKIT, On Poincaré's theorem for fundamental polygons, Adv. Math., 7 (1971), 219-230. Zbl0223.30008MR45 #7049
  13. [12] G. D. MOSTOW, Strong rigidity of locally symmetric spaces, Princeton Univ. Press, 1973, p. 178. Zbl0265.53039MR52 #5874
  14. [13] J. NIELSEN, Untersuchungen zur Topologie der geschlossenen zweiseitige Flächen, Acta Math., 50 (1927), 189-358. Zbl53.0545.12JFM53.0545.12
  15. [14] HARDY and WRIGHT, An Introduction to the Theory of Numbers, Oxford University Press. Zbl0020.29201JFM64.0093.03

Citations in EuDML Documents

  1. Dennis Sullivan, The density at infinity of a discrete group of hyperbolic motions
  2. A. O. Lopes, Ph. Thieullen, Mather measures and the Bowen–Series transformation
  3. Sébastien Alvarez, Nicolas Hussenot, [unknown]
  4. Piotr Bugiel, Distortion inequality for the Frobenius-Perron operator and some of its consequences in ergodic theory of Markov maps in d
  5. B. Stratmann, Mariusz Urbański, The box-counting dimension for geometrically finite Kleinian groups
  6. Frédéric Naud, Expanding maps on Cantor sets and analytic continuation of zeta functions
  7. Thomas A. Schmidt, Rosen fractions and Veech groups, an overly brief introduction
  8. Jean-Claude Picaud, Cohomologie bornée des surfaces et courants géodésiques
  9. Étienne Ghys, Sur l'invariance topologique de la classe de Godbillon-Vey
  10. Sébastien Blachère, Peter Haïssinsky, Pierre Mathieu, Harmonic measures versus quasiconformal measures for hyperbolic groups

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