Disconnected Julia set of Halley's method for exponential maps

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2022-03-06 DOI:10.1080/14689367.2022.2048633

P. Cumsille, J. González–Marín, Gerardo Honorato, Diego Lugo

引用次数: 0

Abstract

We investigate the Halley method of exponential maps. Our main result is that, unlike Newton's method, the Julia set of Halley's method may be disconnected when applied to entire maps of form where p and q are polynomials and q is non-constant. We also describe the nature of the fixed points and classify rational Halley's maps of entire functions.

查看原文本刊更多论文

指数映射的哈雷方法的非连通Julia集

我们研究了指数映射的哈雷方法。我们的主要结果是，与牛顿方法不同，哈雷方法的Julia集在应用于p和q为多项式且q为非常数的整个形式映射时可能是断开的。我们还描述了不动点的性质，并对整个函数的有理哈雷映射进行了分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences