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Dimension of the generalized 4-corner set and its projections

Published online by Cambridge University Press:  10 June 2011

BALÁZS BÁRÁNY
BALÁZS BÁRÁNY*
Affiliation:
Department of Stochastics, Institute of Mathematics, Technical University of Budapest, 1521 Budapest, PO Box 91, Hungary (email: balubsheep@gmail.com)
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Abstract

In the last two decades, considerable attention has been paid to the dimension theory of self-affine sets. In the case of generalized 4-corner sets (see Figure 1), the iterated function systems obtained as the projections of self-affine systems have maps of common fixed points. In this paper, we extend our result [B. Bárány. On the Hausdorff dimension of a family of self-similar sets with complicated overlaps. Fund. Math. 206 (2009), 49–59], which introduced a new method of computation of the box and Hausdorff dimensions of self-similar families where some of the maps have common fixed points. The extended version of our method presented in this paper makes it possible to determine the box dimension of the generalized 4-corner set for Lebesgue-typical contracting parameters.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 4 , August 2012 , pp. 1190 - 1215
Copyright
Copyright © Cambridge University Press 2011

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