منابع مشابه
A characterisation of Newton maps
Conditions are given for a Ck map T to be a Newton map, that is, the map associated with a differentiable real-valued function via Newton’s method. For finitely differentiable maps and functions, these conditions are only necessary, but in the smooth case, i.e. for k = ∞ , they are also sufficient. The characterisation rests upon the structure of the fixed point set of T and the value of the de...
متن کاملNewton maps for quintic polynomials
The purpose of this paper is to study some properties of the Newton maps associated to real quintic polynomials. First using the Tschirnhaus transformation, we reduce the study of Newton’s method for general quintic polynomials to the case f(x) = x − c x + 1. Then we use symbolic dynamics to consider this last case and construct a kneading sequences tree for Newton maps. Finally, we prove that ...
متن کاملNewton maps as matings of cubic polynomials
In this paper we prove existence and uniqueness of matings of a large class of renormalizable cubic polynomials with one fixed critical point and the other cubic polynomial having two fixed critical points. The resulting mating is a Newton map. Our result is the first part towards a conjecture by Tan Lei, stating that all (cubic) Newton maps can be described as matings or captures.
متن کاملBasins of Newton Maps and Asymptotic Values
Newton’s root finding method applied to a (transcendental) entire function f : C → C is the iteration of a meromorphic function Nf . It is well known that if for some starting value z0, Newton’s method converges to a point ξ ∈ C, then f has a root at ξ. We show that in many cases, if an orbit converges to ξ = ∞ for Newton’s method, then f has a ‘virtual root’ at ∞. More precisely, we show that ...
متن کاملA Combinatorial Classification of Postcritically Fixed Newton Maps
We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials and indicate potential for extensions. As our main tool, we show that for a large class of Newton maps that includes all hyperbolic ones, every component of the basin of an attracting fixed point can be connected to ∞ through a finite chain of such components.
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ژورنال
عنوان ژورنال: The ANZIAM Journal
سال: 2006
ISSN: 1446-1811,1446-8735
DOI: 10.1017/s1446181100003047