A special class of infinite measure-preserving quadratic rational maps. Issue 2 (3rd April 2019)

• Record Type: Journal Article
• Authors: Bayless-Rossetti, Rachel; Hawkins, Jane
• Is Part Of: Dynamical systems. Volume 34:Issue 2(2019)
• Page Start: 218
• Page End: 233
• Publication Date: 2019-04-03
• Subjects: Complex dynamics -- Julia sets -- infinite measure; 37F10 -- 26A18 -- 37E99; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2018.1494266
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: We show the existence of a set of positive measure in parameter space, each element corresponding to a rational map of degreed ≥ 2, 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.