- journal article metadata
European Mathematical Society Publishing House
2018-08-30 23:30:01
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
34
2018
3
Connectivity of Julia sets of Newton maps: a unified approach
Krzysztof
Barański
University of Warsaw, Poland
Núria
Fagella
Universitat de Barcelona, Spain
Xavier
Jarque
Universitat de Barcelona, Spain
Bogusława
Karpińska
Warsaw University of Technology, Poland
Newton’s method, root-finding algorithm, iteration, Julia set
In this paper we present a unified proof of the fact that the Julia set of Newton’s method applied to a holomorphic function on the complex plane (a polynomial of degree larger than 1 or a transcendental entire function) is connected. The result was recently completed by the authors’ previous work, as a consequence of a more general theorem whose proof spreads among many papers, which consider separately a number of particular cases for rational and transcendental maps, and use a variety of techniques. In this note we present a unified, direct and reasonably self-contained proof which works in all situations alike.
Functions of a complex variable
Dynamical systems and ergodic theory
1211
1228
10.4171/RMI/1022
http://www.ems-ph.org/doi/10.4171/RMI/1022
8
27
2018