Immediate and Virtual Basins of Newton's Method for Entire Functions

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dc.creatorMayer, Sebastian
dc.creatorSchleicher, Dierk
dc.date2004-03-21
dc.date.accessioned2026-07-07T06:29:32Z
dc.date.available2026-07-07T06:29:32Z
dc.descriptionWe investigate the well known Newton method to find roots of entire holomorphic functions. Our main result is that the immediate basin of attraction for every root is simply connected and unbounded. We also introduce ``virtual immediate basins'' in which the dynamics converges to infinity; we prove that these are simply connected as well.
dc.description9 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0403336
dc.identifierhttp://arxiv.org/abs/math/0403336
dc.identifierAnnales de l'institut Fourier, 56, 2 (2006), 325-336
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98061
dc.subjectDynamical Systems
dc.subject30D05, 37F10, 37N30
dc.titleImmediate and Virtual Basins of Newton's Method for Entire Functions
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