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 |
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| container_title | Dynamical systems (London, England) |
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| creator | Cumsille, Patricio González-Marín, Juan Honorato, Gerardo Lugo, Diego |
| description | 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. |
| doi_str_mv | 10.1080/14689367.2022.2048633 |
| format | Article |
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| subjects | complex dynamics Connectedness Entire functions Mathematical analysis Newton methods Polynomials Primary 37F10 root-finding algorithms Secondary 30D05 |
| title | Disconnected Julia set of Halley's method for exponential maps |
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