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Patterson-Sullivan-type measures on Riccati foliations with quasi-Fuchsian holonomy.
- Source :
-
Bulletin of the Brazilian Mathematical Society . Sep2013, Vol. 44 Issue 3, p393-412. 20p. - Publication Year :
- 2013
-
Abstract
- We consider Riccati foliations ℱ with hyperbolic leaves, over a finite hyperbolic Riemann Surface S, constructed by suspending a representation ρ: π( S) → PSL(2,ℂ) in a quasi-Fuchsian group. The foliated geodesic flow has a repeller-attractor dynamic with generic statistics µ and µ for positive and negative times, respectively. These measures have a common projection to a harmonic measure μ for the Riccati foliation. We describe μ, μ and μ in terms of the Patterson-Sullivan construction, and we show that the measures μ provide examples of the conformal harmonic measures introduced by M. Brunella. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16787544
- Volume :
- 44
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Brazilian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 91660169
- Full Text :
- https://doi.org/10.1007/s00574-013-0018-6