Disconnected Julia set of Halley's method for exponential maps. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Cumsille, Patricio; González-Marín, Juan; Honorato, Gerardo; Lugo, Diego
• Is Part Of: Dynamical systems. Volume 37:Issue 2(2022)
• Page Start: 280
• Page End: 294
• Publication Date: 2022-04-03
• Subjects: Connectedness -- root-finding algorithms -- complex dynamics; Primary 37F10 -- Secondary 30D05 -- 30D20 -- 65H04; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2022.2048633
• Languages: English
• ISSNs: 1468-9367

Abstract

Abstract : We investigate the Halley method of exponential maps. Our main result is that, unlike Newton's method, the Julia set of Halley's method may be disconnected when applied to entire maps of form F = p e q where p and q are polynomials and q is non-constant. We also describe the nature of the fixed points and classify rational Halley's maps of entire functions.