On the question of ergodicity for minimal group actions on the circle
By B. Deroin, V. Kleptsyn, Andrés Navas. 2008
69 citations recorded by the source corpus.
This work is devoted to the study of minimal, smooth actions of finitely generated groups on the circle. We provide a sufficient condition for such an action to be ergodic (with respect to the Lebesgue measure), and we illustrate this condition by studying two relevant examples. Under an analogous hypothesis, we also deal with the problem of the zero Lebesgue measure for exceptional minimal sets. This hypothesis leads to many other interesting conclusions, mainly concerning the stationary and conformal measures. Moreover, several questions are left open. The methods work as well for codimension-one foliations, though the results for this case are not explicitly stated.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/73f7d0696955675687ed5ddb784940d6f1b48a2b
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Harmonic measures versus quasiconformal measures for hyperbolic groups (2008, background): “Since vG = 1, this means that ν̂ has maximal dimension in the boundary of (Γ, dG) endowed with a visual metric.”
- GROUP ACTIONS ON 1-MANIFOLDS: A LIST OF VERY CONCRETE OPEN QUESTIONS (2017, background): “to Furstenberg [46] solves this question for lattices in PSL(2;R). However, this strongly relies on the geometry of the Poincare disk, and does not extend to general groups. Moreover, it is shown in [35, 60] (see also [8]) that the resulting probability measure is singular with respect to the Lebesg”