Persistence landscapes of affine fractals

• Autorzy: Catanzaro Michael J. , Przybylski Lee , Weber Eric S.

Identyfikatory

DOI

10.1515/dema-2022-0015

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

persistent homology; persistence landscapes; affine fractal; Cantor set

PL

homologia; krajobraz; fraktal; zbiór Cantora

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 163--192
• Opis fizyczny: Bibliogr. 40 poz., rys.

Twórcy

autor

Catanzaro Michael J.

• Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, IA 50011, United States

autor

Przybylski Lee

• Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, IA 50011, United States

autor

Weber Eric S.

• Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, IA 50011, United States

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Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).