Parabolic iterated function systems

In this paper we introduce and explore conformal parabolic iterated functio n systems. We define and study topological pressure, Perron-Frobenius-type operators, semiconformal and conformal measures and the Hausdorff dimension of the limit set. With every parabolic system we associate an infinite hyp erbolic conformal iterated function system and we employ it to study geomet ric and dynamical features (properly defined invariant measures for example ) of the limit set.