[Actions linéaires des groupes libres]
Dans cet article nous étudions les propriétés dynamiques des actions linéaires des groupes libres par l'action induite sur l'espace projectif. Ce point de vue nous permet de présenter des techniques du formalisme thermodynamique. En particulier, nous obtenons des estimations sur les croissances des orbites et leurs distributions limites sur l'espace projectif.
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.
Keywords: linear action, free group, projective space, thermodynamic formalism, orbit counting
Mot clés : action linéaire, groupe libre, espace projectif, formalisme thermodynamique, compte d'orbites
@article{AIF_2001__51_1_131_0,
author = {Pollicott, Mark and Sharp, Richard},
title = {Linear actions of free groups},
journal = {Annales de l'Institut Fourier},
pages = {131--150},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {51},
number = {1},
year = {2001},
doi = {10.5802/aif.1819},
mrnumber = {1821072},
zbl = {0967.37016},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1819/}
}
TY - JOUR AU - Pollicott, Mark AU - Sharp, Richard TI - Linear actions of free groups JO - Annales de l'Institut Fourier PY - 2001 SP - 131 EP - 150 VL - 51 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1819/ DO - 10.5802/aif.1819 LA - en ID - AIF_2001__51_1_131_0 ER -
%0 Journal Article %A Pollicott, Mark %A Sharp, Richard %T Linear actions of free groups %J Annales de l'Institut Fourier %D 2001 %P 131-150 %V 51 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1819/ %R 10.5802/aif.1819 %G en %F AIF_2001__51_1_131_0
Pollicott, Mark; Sharp, Richard. Linear actions of free groups. Annales de l'Institut Fourier, Tome 51 (2001) no. 1, pp. 131-150. doi : 10.5802/aif.1819. http://www.numdam.org/articles/10.5802/aif.1819/
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