Linear actions of free groups

Mark Pollicott[1]; Richard Sharp[1]

  • [1] University of Manchester, Department of Mathematics, Oxford Road, Manchester M13 9PL (Grande-Bretagne)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 1, page 131-150
  • ISSN: 0373-0956

Abstract

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In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.

How to cite

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Pollicott, Mark, and Sharp, Richard. "Linear actions of free groups." Annales de l’institut Fourier 51.1 (2001): 131-150. <http://eudml.org/doc/115906>.

@article{Pollicott2001,
abstract = {In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.},
affiliation = {University of Manchester, Department of Mathematics, Oxford Road, Manchester M13 9PL (Grande-Bretagne); University of Manchester, Department of Mathematics, Oxford Road, Manchester M13 9PL (Grande-Bretagne)},
author = {Pollicott, Mark, Sharp, Richard},
journal = {Annales de l’institut Fourier},
keywords = {linear action; free group; projective space; thermodynamic formalism; orbit counting},
language = {eng},
number = {1},
pages = {131-150},
publisher = {Association des Annales de l'Institut Fourier},
title = {Linear actions of free groups},
url = {http://eudml.org/doc/115906},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Pollicott, Mark
AU - Sharp, Richard
TI - Linear actions of free groups
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 1
SP - 131
EP - 150
AB - In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.
LA - eng
KW - linear action; free group; projective space; thermodynamic formalism; orbit counting
UR - http://eudml.org/doc/115906
ER -

References

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  1. J. Dani, Density properties of orbits under discrete groups, J. Indian Math. Soc. 39 (1976), 189-217 Zbl0428.22006MR444570
  2. W. Ellison, F. Ellison, Prime Numbers, (1985), Wiley, New York Zbl0624.10001MR814687
  3. L. Greenberg, Flows on homogeneous spaces, 53 (1963), 85-103, Princeton Univ. Press, Princeton, N.J. Zbl0106.36802
  4. P. de la Harpe, Free groups in linear groups, Enseign. Math. 29 (1983), 129-144 Zbl0517.20024MR702736
  5. T. Kato, Perturbation Theory for Linear Operators, (1976), Springer Verlag, Berlin Zbl0148.12601MR407617
  6. S. Lalley, Renewal theorems in symbolic dynamics, with applications to geodesic flows, non-Euclidean tessellations and their fractal limits, Acta. Math. 163 (1989), 1-55 Zbl0701.58021MR1007619
  7. W. Parry, M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque (1990), 1-268 Zbl0726.58003MR1085356
  8. S.J. Patterson, The limit set of a Fuchsian group, Acta. Math. 136 (1976), 241-273 Zbl0336.30005MR450547
  9. M. Pollicott, R. Sharp, Comparison theorems and orbit counting in hyperbolic geometry, Trans. Amer. Math. Soc. 350 (1998), 473-499 Zbl0909.20023MR1376553
  10. D. Ruelle, Thermodynamic Formalism, (1978), Addison Wesley, Redding, Mass. Zbl0401.28016MR511655
  11. D. Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 171-202 Zbl0439.30034MR556586
  12. J. Tits, Free subgroups in linear groups, J. Algebra 20 (1972), 250-270 Zbl0236.20032MR286898
  13. M. Wojtkowski, On uniform contraction generated by positive matrices, Random matrices and their applications (Brunswick, Maine, 1984) 50 (1986), 109-118, Amer. Math. Soc., Providence, R.I. Zbl0584.60017

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