Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 3, pp. 367--385

LIMIT SETS OF GROUPS OF LINEAR TRANSFORMATIONS

By

J.-P. CONZE and Y. GUIVARC'H, *Université de Rennes, France*

*SUMMARY. *For a subgroup G of the
linear group of **R**^{d}, we describe the G-orbit closures of
points of **R**^{d} in terms of the limit set of G in the
projective space **P**^{d-1}, under proximality and irreducibility
conditions. In particular, we show the minimality of the action of
G on the corresponding asymptotic set in the linear space
when G is a Schottky group.

*AMS (1991) subject classification. * 58F17, 54H20,
22E40.

*Key words and phrases. *Asymptotic set, limit point,
proximality, dominant eigenvector, horocycle flow, Schottky
groups.