Annales Academię Scientiarum Fennicę
Volumen 35, 2010, 335-350


Vadim A. Kaimanovich

University of Ottawa, Department of Mathematics and Statistics
585 King Edward Ave, Ottawa ON, K1N 6N5, Canada; vkaimano 'at'

Abstract. By looking at the relationship between the recurrence properties of a countable group action with a quasi-invariant measure and the structure of the space of ergodic components, we establish a simple general description of the Hopf decomposition of the action into its conservative and dissipative parts in terms of the Radon-Nikodym derivatives. As an application we describe the conservative part of the boundary action of a discrete group of isometries of a Gromov hyperbolic space with respect to an invariant quasi-conformal stream.

2000 Mathematics Subject Classification: Primary 37A20; Secondary 22F10, 28D99, 30F40, 53C20.

Key words: Conservative action, dissipativity, recurrent set, wandering set, Hopf decomposition, ergodic components, Gromov hyperbolic space, horospheric limit set.

Reference to this article: V.A. Kaimanovich: Hopf decomposition and horospheric limit sets. Ann. Acad. Sci. Fenn. Math. 35 (2010), 335-350.

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