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Sibirsk. Mat. Zh., 2012, Volume 53, Number 4, Pages 794–804 (Mi smj2364)  

The fractal “Frog”

A. Gospodarczyk

Institute of Mathematics, University of Gdańsk, Gdańsk, Poland

Abstract: In [1–3] some analytical properties were investigated of the Von Koch curve $\Gamma_\theta$, $\theta\in(0,\frac\pi4)$. In particular, it was shown that $\Gamma_\theta$ is quasiconformal and not AC-removable. The natural question arises: Can one find a quasiconformal and not AC-removable curve essentially different from $\Gamma_\theta$ in the sense that it is not diffeomorphic to $\Gamma_\theta$? The present paper is an answer to the question. Namely, we construct a quasiconformal curve, calling the “Frog”, which is not AC-removable and not diffeomorphic to $\Gamma_\theta$ for any $\theta\in(0,\frac\pi4)$.

Keywords: Sierpiński gasket, Frog, quasiconformal curve, fractals, iterated function system, $BL^\beta$-spaces, Hausdorff dimension, AC-removability, Von Koch curve, diffeomorphism.

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English version:
Siberian Mathematical Journal, 2012, 53:4, 635–644

Bibliographic databases:

UDC: 517.518.1+517.518.17
Received: 03.09.2011

Citation: A. Gospodarczyk, “The fractal “Frog””, Sibirsk. Mat. Zh., 53:4 (2012), 794–804; Siberian Math. J., 53:4 (2012), 635–644

Citation in format AMSBIB
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\paper The fractal ``Frog''
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\pages 794--804
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  • Сибирский математический журнал Siberian Mathematical Journal
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