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On quasi-invariant transverse measures for the horospherical foliation of a negatively curved manifold

Published online by Cambridge University Press:  02 February 2004

BARBARA SCHAPIRA
BARBARA SCHAPIRA
Affiliation:
MAPMO, Université d'Orléans, Rue de Chartres, BP 6759, 45067 Orléans Cedex 2, France (e-mail: schapira@labomath.univ-orleans.fr)
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Abstract

If M is a compact or convex-cocompact negatively curved manifold, we associate to any Gibbs measure on T1M a quasi-invariant transverse measure for the horospherical foliation, and prove geometrically that this measure is uniquely determined by its Radon–Nikodym cocycle. (This extends the Bowen–Marcus unique ergodicity result for this foliation.) We shall deduce from this result some equidistribution properties for the leaves of the foliation with respect to these Gibbs measures. We use it also in the study of invariant measures for horospherical foliations on regular covers of M.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 1 , February 2004 , pp. 227 - 255
Copyright
2004 Cambridge University Press

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