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The Hausdorff dimension of self-similar sets under a pinching condition


Author: Xiao Ping Gu
Journal: Proc. Amer. Math. Soc. 118 (1993), 1281-1289
MSC: Primary 28A78; Secondary 58F11
DOI: https://doi.org/10.1090/S0002-9939-1993-1181166-1
MathSciNet review: 1181166
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Abstract: We study self-similar sets in the case where the construction diffeomorphisms are not necessarily conformal. Using topological pressure we give an upper estimate of the Hausdorff dimension, when the construction diffeomorphisms are $ {C^{1 + \kappa }}$ and satisfy a $ \kappa $-pinching condition for some $ \kappa \leqslant 1$. Moreover, if the construction diffeomorphisms also satisfy the disjoint open set condition we then give a lower bound for the Hausdorff dimension.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1181166-1
Article copyright: © Copyright 1993 American Mathematical Society

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