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 Rd, we describe the G-orbit closures of points of Rd in terms of the limit set of G in the projective space Pd-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.

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