A special class of infinite measure-preserving quadratic rational maps

Abstract

ABSTRACTWe show the existence of a set of positive measure in parameter space, each element corresponding to a rational map of degree , for which there exists an invariant infinite σ-finite measure equivalent to a conformal measure. These maps are conservative and exact with respect to the invariant measure, and are perturbations of generalized Boole maps and inner functions. For quadratic Boole maps of with real coefficients we show that the Krengel entropy provides a complete invariant for c-isomorphism classes of quadratic maps of this type.