99-407 J. Buzzi, F. Paccaut, B. Schmitt

Conformal measures for multidimensional piecewise invertible maps (505K, Postscript) Oct 26, 99

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Abstract. Given a piecewise invertible map T:X-->X and a weight g:X-->(0,infty), a conformal measure nu is a probability measure such that, for all measurable A subset X with T|A one-to-one, nu(TA) = lambda int_A (1/g) dnu with lambda a positive constant. Such a measure is an essential tool for the study of equilibrium states. In this paper we build such a conformal measure, assuming essentially that the topological pressure of the boundary is small and that log g has bounded distortion.

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