Annales Academię Scientiarum Fennicę

Mathematica

Volumen 35, 2010, 335-350

# HOPF DECOMPOSITION AND HOROSPHERIC LIMIT SETS

## Vadim A. Kaimanovich

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.

Full document as PDF file

doi:10.5186/aasfm.2010.3522

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