Title: Attractor of generalised countable ultrametrisable iterated function system through Gromov-Hausdorff ultrametric

Authors: M. Priya; R. Uthayakumar

Addresses: Department of Mathematics, The Gandhigram Rural Institute – Deemed to be University, Gandhigram, Dindigul, TamilNadu – 624 302, India ' Department of Mathematics, The Gandhigram Rural Institute – Deemed to be University, Gandhigram, Dindigul, TamilNadu – 624 302, India

Abstract: In the disciplines like matching of articulated objects, molecular biology, and face recognition, the advantage of shape acquisition and modelling results in greater attention. An optimal approach to handling these shape matching and recognition issues is Gromov-Hausdorff distance, a technique to identify the similarity between shapes. Noting the major contribution of this special metric, this article shows its interest to derive a fixed point theorem on the complete ultrametric space for a cyclic (α-β)-contraction. With this new fixed point theorem and a few additional results, this study defines the ideology of a generalised countable ultrametrisable iterated function system, and the description of the generalised Hutchinson-Barnsley operator is provided. Finally, the classical Hutchinson-Barnsley theorem (HB theorem, for short) employed in the newly formulated iterated function system shows the fractal set of the iterated function system (simply IFS).

Keywords: Gromov-Hausdorff ultrametric space; Gromov-Hausdorff distance; iterated function system; IFS; attractor; fractal; HB theory.

DOI: 10.1504/IJANS.2024.141350

International Journal of Applied Nonlinear Science, 2024 Vol.4 No.3, pp.228 - 240

Received: 03 Aug 2023
Accepted: 15 Mar 2024
Published online: 09 Sep 2024 *

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