... Julia sets for the standard Newton's method, Halley's method, and Schroder's method. Appl. Math. Comput. 189(2), 1186–1195 (2007) W.F. Yang, Symmetries of the Julia sets of Newton's method for multiple root. Appl. Math. Comput. 217(6) ...
... Julia set generated by fractional Lotka-Volterra models. Commun Nonlinear Sci Numer Simul 72:417–431 402. Liu S ... Symmetries of the Julia sets of Newton's method for multiple root. Appl Math Comput 217:2490–2494 419. Mandelbrot B ...
... Newton's method to the complex polynomial equation P2 ( z ) = z2 -λ = 0 ( Chances are that you would not use Newton's method to find the roots of this polynomial , but ... ) . The Newton iteration function is then given by N2 ( z ) = z ...
... Newton's method that converge to the root at 1 for the cubic equationz 3 −1. The initial conditions for the other ... Julia set: it is mapped into itself and is the border between the two domains of attraction. At the end of his ...
... method . Suppose we are applying Newton's method to find the roots of a family of polyno- mials P 、 which has a multiple root ... Julia set of Fo , which will be defined below . For most of this paper , the singularly perturbed family will ...
... method to the high level of robustness and effectiveness as the Cluster-Adapted Method package can be found in [5] ... Julia sets. In the specific case of two roots, the roots' basins of attraction are separated by the right ...
... Julia sets for other functions , and Mandelbrot sets for other families of functions . Here are some interesting ... root of unity w is a critical point , but each of the 2n critical orbits behaves in the same way . Hence the ...
... set of singularities ( épines , sinks ) of A. The main results of the paper are the following theorems . Theorem 1. An expansive attractor A can be decomposed into the following invariant sets : A = pHUWa ( E ) US , where pH is a compact ...
... root-finding methods, J. of Comp. and Appl. Math. 130, pp. 197–204. Kalantari, B. and Pate, T. H. (2001). A determinantal lower bound, Linear Algebra and its Application 326, pp. 151–159. Kneisl, K. (2001). Julia sets for the super-Newton ...
Introduction Fundamental properties of Newton maps Invariant 3-manifolds associated to invariant circles The behavior at infinity when $a=b=0$ The Farey blow-up The compactification when $a=b=0$ The case where $a$ and $b$ are arbitrary ...