On properties of similarity boundary of attractors in product dynamical systems

<p style='text-indent:20px;'><i>Fractals</i> in higher dimensional <i>dynamical systems</i> have significant roles physics and other applied sciences. In this paper, one of the key property fractals, called <i>self similarity</i> product systems, is studied using concept <i>similarity boundary</i>. The relationship between similarity boundary an attractor a space to its projection spaces discussed. impact <i>inverse invariance</i> on coordinate iterated function system analyzed. Fractals satisfying <i>strong open set condition</i>, restricted attractors spaces, are characterized. their overlapping sets also obtained. equivalency condition (ROSC) strong proved. Self characterized Hausdorff measure boundary. Also, dimensions for different types systems obtained.</p>