Disconnected Julia set of Halley's method for exponential maps

Disconnected Julia set of Halley's method for exponential maps

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 where p and q are polynomials and q is non-constant. We also describe the nature of the fixed poin...

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Veröffentlicht in:Dynamical systems (London, England) England), 2022-04, Vol.37 (2), p.280-294
Hauptverfasser: Cumsille, Patricio, González-Marín, Juan, Honorato, Gerardo, Lugo, Diego
Format: Artikel
Sprache:eng
Schlagworte:
complex dynamics
Connectedness
Entire functions
Mathematical analysis
Newton methods
Polynomials
Primary 37F10
root-finding algorithms
Secondary 30D05
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Beschreibung
Zusammenfassung: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 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.
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2022.2048633