CHAOS IN TERMS OF THE MAP CHI-]OMEGA(CHI, F)

被引：34

作者：

BRUCKNER, AM

CEDER, J

机构：

[1] University of California, Santa Barbara, CA

来源：

PACIFIC JOURNAL OF MATHEMATICS | 1992年 / 156卷 / 01期

关键词：

D O I：

10.2140/pjm.1992.156.63

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be the class of compact subsets of I = [0, 1] , furnished with the Hausdorf metric. Let f is-an-element-of C(I, I) . We study the map omega(f) : I --> K defined as omega(f)(x) = omega(x ,f), the omega-limit set of x under f . This map is rarely continuous, and is always in the second Baire class. Those f for which omega(f) is in the first Baire class exhibit a form of nonchaos that allows scrambled sets but not positive entropy. This class of functions can be characterized as those which have no infinite omega-limit sets with isolated points. We also discuss methods of constructing functions with zero topological entropy exhibiting infinite omega-limit sets with various properties. 4

引用

页码：63 / 96

页数：34