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This content will become publicly available on January 1, 2023

Title: Persistence landscapes of affine fractals
Abstract We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes, which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.
Authors:
; ;
Award ID(s):
1830254 1934884
Publication Date:
NSF-PAR ID:
10329468
Journal Name:
Demonstratio Mathematica
Volume:
55
Issue:
1
Page Range or eLocation-ID:
163 to 192
ISSN:
2391-4661
Sponsoring Org:
National Science Foundation
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