no. 1
Linear actions of free groups
[Actions linéaires des groupes libres]
Pollicott, Mark1 ; Sharp, Richard1
1 University of Manchester, Department of Mathematics, Oxford Road, Manchester M13 9PL (Grande-Bretagne)
Annales de l'Institut Fourier, Tome 51 (2001) no. 1, pp. 131-150.

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.

DOI : 10.5802/aif.1819
Classification : 37C35, 37C85, 37D35, 20G20
Keywords: linear action, free group, projective space, thermodynamic formalism, orbit counting
Mot clés : action linéaire, groupe libre, espace projectif, formalisme thermodynamique, compte d'orbites

Pollicott, Mark 1 ; Sharp, Richard 1

1 University of Manchester, Department of Mathematics, Oxford Road, Manchester M13 9PL (Grande-Bretagne) 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.1819/

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