---
res:
bibo_abstract:
- "We study rigidity of rational maps that come from Newton's root finding method
for polynomials of arbitrary degrees. We establish dynamical rigidity of these
maps: each point in the Julia set of a Newton map is either rigid (i.e. its orbit
can be distinguished in combinatorial terms from all other orbits), or the orbit
of this point eventually lands in the filled-in Julia set of a polynomial-like
restriction of the original map. As a corollary, we show that the Julia sets of
Newton maps in many non-trivial cases are locally connected; in particular, every
cubic Newton map without Siegel points has locally connected Julia set.\r\nIn
the parameter space of Newton maps of arbitrary degree we obtain the following
rigidity result: any two combinatorially equivalent Newton maps are quasiconformally
conjugate in a neighborhood of their Julia sets provided that they either non-renormalizable,
or they are both renormalizable “in the same way”.\r\nOur main tool is a generalized
renormalization concept called “complex box mappings” for which we extend a dynamical
rigidity result by Kozlovski and van Strien so as to include irrationally indifferent
and renormalizable situations.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Kostiantyn
foaf_name: Drach, Kostiantyn
foaf_surname: Drach
foaf_workInfoHomepage: http://www.librecat.org/personId=fe8209e2-906f-11eb-847d-950f8fc09115
orcid: 0000-0002-9156-8616
- foaf_Person:
foaf_givenName: Dierk
foaf_name: Schleicher, Dierk
foaf_surname: Schleicher
bibo_doi: 10.1016/j.aim.2022.108591
bibo_volume: 408
dct_date: 2022^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0001-8708
dct_language: eng
dct_publisher: Elsevier@
dct_subject:
- General Mathematics
dct_title: Rigidity of Newton dynamics@
...