On a Topological Problem of Strange Attractors

الأصل · EN

Somehow, the revised version of our paper 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× n matrix (i.e., all of its eigenvalues have moduli >1) and a finite set of vectors in Zⁿ. We concentrate on the problem of connectedness for n≤ 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.