ON PLANAR PIECEWISE AND TWO-TORUS PARABOLIC MAPS

Author:

ASHWIN PETER1,FU XINCHU2,LIN CONGPING23

Affiliation:

1. Mathematics Research Institute, University of Exeter, Exeter EX4 4QF, UK

2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China

3. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

Abstract

We investigate properties and examples of iterated planar piecewise parabolic (PWP) maps, including those induced by two-torus parabolic maps and their inverses. PWP maps are area-preserving maps that have constant linearizations but only one eigenvector with eigenvalue one. We obtain necessary and sufficient conditions for a two-torus parabolic map to be invertible. For noninvertible PWP maps, there are a number of questions about the existence and structure of attractors for such maps. We introduce the simplest example of a nontrivial PWP map, defined by a parabolic linear map with a translation that is a different constant on each side of a given line in the plane. For this "half plane parabolic map" we obtain sufficient conditions for a bounded attractor to exist, discuss their dynamical properties and give some examples of these and related maps.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3