Hopf decomposition and horospheric limit sets

Details Hopf decomposition and horospheric limit sets Hopf decomposition and horospheric limit sets

2008-07-07

arxiv.org/abs/0807.0995v1

Mathematics

Dynamical Systems

Scientific paper

By looking at the relationship between the recurrence properties of a countable group action with a quasi-invariant measure and the structure of its ergodic components we establish a simple general description of the Hopf decomposition of the action into the conservative and the dissipative parts in terms of the Radon--Nikodym derivatives of the action. As an application we prove that the conservative part of the boundary action of a discrete group of isometries of a Gromov hyperbolic space with respect to any invariant quasi-conformal stream coincides (mod 0) with the big horospheric limit set of the group.

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