Parameterized curve as attractors of some countable iterated function systems

Nicolae-Adrian Secelean

Address.
  Department of Mathematics, ``Lucian Blaga" University of Sibiu, Romania
 

E-mail. secelean@mail.ulbsibiu.ro

Abstract.
In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J.~E.~Hutchinson \cite{Hut81}.

AMSclassification. Primary 28A80, Secondary 37C70, 47H10.

Keywords.  Hausdorff metric, countable iterated function system, attractor.