Critical intermittency in rational maps

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-05-08 DOI:10.1088/1361-6544/ad42f9

Ale Jan Homburg, Han Peters, Vahatra Rabodonandrianandraina

引用次数: 0

Abstract

Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in iterated function systems, and involves a superattracting periodic orbit. This paper will provide and study examples of iterated function systems by two rational maps on the Riemann sphere that give rise to critical intermittency. The main ingredient for this is a superattracting fixed point for one map that is mapped onto a common repelling fixed point by the other map. We include a study of topological properties such as topological transitivity.

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理性地图的临界间歇性

间歇动力学的特点是长时间存在不同类型的动力学特征，例如几乎是周期性的动力学与混沌动力学交替出现。临界间歇是迭代函数系统中可能出现的间歇动力学，涉及超吸引周期轨道。本文将提供并研究黎曼球上两个有理映射迭代函数系统的例子，这些例子会引起临界间歇性。其主要因素是一个映射的超吸引定点被另一个映射映射到一个共同排斥定点上。我们还研究了拓扑性质，如拓扑反证法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.