Intermingled basins for the triangle map

被引：25

作者：

Alexander, JC

Hunt, BR

Kan, I

Yorke, JA

机构：

[1] UNIV MARYLAND,DEPT MATH,COLLEGE PK,MD 20742

[2] UNIV MARYLAND,INST PHYS SCI & TECHNOL,COLLEGE PK,MD 20742

[3] GEORGE MASON UNIV,DEPT MATH,FAIRFAX,VA 22030

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 1996年 / 16卷

关键词：

D O I：

10.1017/S0143385700009020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A family of quadratic maps of the plane has been found numerically for certain parameter values to have three attractors, in a triangular pattern, with 'intermingled' basins. This means that for every open set S, if the basin of attraction of one of the attractors intersects S in a set of positive Lebesgue measure, then so do the other two basins. In this paper we mathematically verify this observation for a particular parameter, and prove that our results hold for a set of parameters with positive Lebesgue measure.

引用

页码：651 / 662

页数：14

共 12 条

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