Annales Academię Scientiarum Fennicę
Mathematica
Volumen 35, 2010, 335-350
University of Ottawa, Department of Mathematics and Statistics
585 King Edward Ave,
Ottawa ON, K1N 6N5, Canada;
vkaimano 'at' uottawa.ca
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.
doi:10.5186/aasfm.2010.3522
Copyright © 2010 by Academia Scientiarum Fennica