University of Oulu

Continuity of subadditive pressure for matrix cocycles and the dimension of a self-affine set

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Author: Kormu, Jussi1
Organizations: 1University of Oulu, Faculty of Science, Mathematics
Format: ebook
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
Pages: 56
Persistent link:
Language: English
Published: Oulu : J. Kormu, 2016
Publish Date: 2016-04-26
Thesis type: Master's thesis
Tutor: Järvenpää, Esa
Reviewer: Järvenpää, Esa
Suomala, Ville
The pressure function P(A,s) and singularity dimension s(A) are closely related to the dimension of a typical self affine set. De-Jun Feng and Pablo Shmerkin proved in their article “Non-conformal repellers and continuity of pressure for matrix cocycles” that P(A,s) and s(A) depend continuously on the linear maps A. This is achieved by proving the continuity of a more general pressure for matrix cocycles. In this thesis we proof these continuity results following the arguments of Feng and Shmerkin. Compared to the original article the proofs are given with greater details and more necessary background is covered.
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Copyright information: © Jussi Kormu, 2016. This publication is copyrighted. You may download, display and print it for your own personal use. Commercial use is prohibited.