We study numerically the α- and ω-limits of the Newton maps of quadratic polynomial transformations of the plane into itself.

We show how Newton's method for finding the roots of a real function f leads to chaotic dynamics (infinitely many periodic points and positive topological ...

Oct 22, 2024 · We study numerically the α- and ω-limits of the Newton maps of quadratic polynomial transformations of the plane into itself.

Dynamics of Newton Maps of Quadratic Polynomial Maps of ℝ2 into Itself // International Journal of Bifurcation and Chaos in Applied Sciences and Engineering.

Abstract: We study numerically the α - and ω -limits of the Newton maps of quadratic polynomial transformations of the plane into itself.

The main goal of the present article is exactly to study in detail a single case, the one of Newton maps of polynomial transformations of the plane into itself ...

Aug 14, 2021 · We consider all the quadratic Newton maps including those conformally con- jugate to polynomials and describe their dynamics completely. It ...

Given the rich behavior of holomorphic Newton maps on R2, it is natural to ask what happens in case of non-holomorphic ones, namely Newton maps of polynomial ...

In this paper, we will study Newton's method for solving two simultaneous quadratic equations in two variables. In one dimension, if F is a polynomial, ...

Our work is an attempt to describe the Berkovich dynamics of certain class of higher degree rational maps following quadratic case given by Kiwi [17] and ...