On the dimension of self-affine sets and measures with overlaps
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- by Balázs Bárány, MichałRams and Károly Simon PDF
- Proc. Amer. Math. Soc. 144 (2016), 4427-4440 Request permission
Abstract:
In this paper we consider diagonally affine, planar IFS $\Phi =$ $\{S_i(x,y)\!=\!(\alpha _ix+t_{i,1},\beta _iy+t_{i,2})\}_{i=1}^m$. Combining the techniques of Hochman and Feng and Hu, we compute the Hausdorff dimension of the self-affine attractor and measures and we give an upper bound for the dimension of the exceptional set of parameters.References
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Additional Information
- Balázs Bárány
- Affiliation: MTA-BME Stochastics Research Group, Budapest University of Technology and Economics, P.O. Box 91, 1521 Budapest, Hungary — and — University of Warwick, Mathematics Institute, Coventry CV4 7AL, United Kingdom
- MR Author ID: 890989
- Email: balubsheep@gmail.com
- MichałRams
- Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland
- Email: rams@impan.pl
- Károly Simon
- Affiliation: Department of Stochastics, Institute of Mathematics, Budapest University of Technology and Economics, P.O. Box 91, 1521 Budapest, Hungary
- MR Author ID: 250279
- Email: simonk@math.bme.hu
- Received by editor(s): April 27, 2015
- Received by editor(s) in revised form: December 23, 2015
- Published electronically: June 10, 2016
- Additional Notes: The research of the first and third authors was partially supported by the grant OTKA K104745. The research of the first author was partially supported by the grant EP/J013560/1. The second author was supported by National Science Centre grant 2014/13/B/ST1/01033 (Poland). This work was partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.
- Communicated by: Nimish A. Shah
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4427-4440
- MSC (2010): Primary 28A80; Secondary 28A78
- DOI: https://doi.org/10.1090/proc/13121
- MathSciNet review: 3531192