On a Topological Problem of Strange Attractors

Abstract

Somehow, the revised version of our paper \cite{KY} does not appear on journals' home page. Here we present the revised version altered to reflect the corrections and/or additions to that paper. In this note, we consider self-affine attractors that are generated by an integer expanding $n\times n$ matrix (i.e., all of its eigenvalues have moduli $>1$) and a finite set of vectors in ${\Bbb{Z}}^n$. We concentrate on the problem of connectedness for $n\leq 2$. Although, there has been intensive study on the topic recently, this problem is not settled even in the one-dimensional case. We focus on some basic attractors, which have not been studied fully, and characterize connectedness.