J. Buzzi, F. Paccaut, B. Schmitt
Conformal measures for multidimensional piecewise invertible maps
(505K, Postscript)
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.