Typical dynamics of Newton's method (vol 318, 108201, 2022)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10492785" target="_blank" >RIV/00216208:11320/24:10492785 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FSFTY4q-8e" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FSFTY4q-8e</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2024.108986" target="_blank" >10.1016/j.topol.2024.108986</a>

Result language
angličtina
Original language name
Typical dynamics of Newton's method (vol 318, 108201, 2022)
Original language description
Let C (1) ( M ) be the space of continuously differentiable real-valued functions defined on [ - M, M ]. Here, we address an irremediable flaw found in [4], and show that for the typical element f in C (1) ( M ), there exists a set S subset of [ - M, M ], both residual and of full measure in [ - M, M ], such that for any x is an element of S , the trajectory generated by Newton's method using f and x either diverges, converges to a root of f , or generates a Cantor set as its attractor. Whenever the Cantor set is the attractor, the dynamics on the attractor are described by a single type of adding machine, so that the dynamics on all of these attracting Cantor sets are topologically equivalent. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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