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Multifractal analysis on the flexed Sierpiński gasket

Published online by Cambridge University Press:  13 May 2005

KRZYSZTOF BARAŃSKI
KRZYSZTOF BARAŃSKI
Affiliation:
Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland (e-mail: baranski@mimuw.edu.pl)Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, PO Box 21, 00-956 Warszawa 10, Poland.
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Abstract

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We determine the Hausdorff and box dimensions of the flexed Sierpiński gasket $\Lambda$, which is the limit set for a non-Moran-like non-affine geometric construction in the plane. We also provide a multifractal formalism for the Bernoulli measures on $\Lambda$, computing explicitly the pointwise dimension spectra.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 3 , June 2005, pp. 731 - 757
Copyright
2005 Cambridge University Press