--- 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_issue: Part A bibo_volume: 408 dct_date: 2022^xs_gYear dct_identifier: - UT:000860924200005 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@ ...