Advertisement

Finitely Supported Measures on \(S{L}_{2}(\mathbb{R})\) Which are Absolutely Continuous at Infinity

  • Jean BourgainEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)

Abstract

We construct finitely supported symmetric probability measures on \(S{L}_{2}(\mathbb{R})\) for which the Furstenberg measure on \({\mathbb{P}}_{1}(\mathbb{R})\) has a smooth density.

Keywords

Probability Measure Haar Measure Projective Action Absolute Continuity Similar Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author is grateful to C. McMullen and P. Varju for several related discussions. Research was partially supported by NSF grants DMS-0808042 and DMS-0835373

References

  1. 1.
    B. Barany, M. Pollicott, K. Simon, Stationary measures for projective transformations: The Blackwell and Furstenberg measures. Preprint (2010)Google Scholar
  2. 2.
    J. Bourgain, Expanders and dimensional expansion. C.R. Math. Acad. Sci. Paris 347(7–8), 356–362 (2000)Google Scholar
  3. 3.
    J. Bourgain, A. Gamburd, On the spectral gap for finitely generated subgroups of SU(2). Invent. Math. 171(1), 83–121 (2008)Google Scholar
  4. 4.
    V. Kaimanovich, V. Le Prince, Matrix random products with singular harmonic measure. Geom. Ded. 150, 257–279 (2011)Google Scholar
  5. 5.
    K. Simon, B. Solomyak, M. Urbanski, Hausdorff dimension of limit sets for parabolic IFS with overlap. Pac. J. Math. 201(2), 441–478 (2001)Google Scholar
  6. 6.
    K. Simon, B. Solomyak, M. Urbanski, Invariant measures for parabolic IFS with overlaps and random continued fractions. Trans. Am. Math. Soc. 353(12), 5145–5164 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA

Personalised recommendations