On boundaries of attractors in dynamical systems

Fractal geometry is one of the beautiful and challenging branches of mathematics. Self similarity is an important property, exhibited by most of the fractals. Several forms of self similarity have been discussed in the literature. Iterated Function System (IFS) is a mathematical scheme to generate fractals. There are several variants of IFSs such as condensation IFS, countable IFS, etc. In this paper, certain properties of self similar sets, using the concept of boundary are discussed. The notion of boundaries like similarity boundary and dynamical boundary are extended to condensation IFSs. The relationships and measure theoretic properties of boundaries in dynamical systems are analyzed. Self similar sets are characterized using the Hausdorff measure of their boundaries towards the end. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper explores the concept of self similarity in fractal geometry and the use of Iterated Function Systems (IFS) to generate fractals. Different variants of IFSs and boundary concepts are discussed in relation to self similar sets. The characterization of self similar sets using the Hausdorff measure of boundaries is also examined towards the end.