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• W2039148753 abstract "We develop a thermodynamic formalism for quasi-multiplicative potentials on a countable symbolic space and apply these results to the dimension theory of infinitely generated self-affine sets. The first application is a generalisation of Falconer's dimension formula to include typical infinitely generated self-affine sets and show the existence of an ergodic invariant measure of full dimension whenever the pressure function has a root. Considering the multifractal analysis of Birkhoff averages of general potentials $Phi$ taking values in $R^{N}$, we give a formula for the Hausdorff dimension of $J_Phi(alpha)$, the $alpha$-level set of the Birkhoff average, on a typical infinitely generated self-affine set. We also show that for bounded potentials $Phi$, the Hausdorff dimension of $J_Phi(alpha)$ is given by the maximum of the critical value for the pressure and the supremum of Lyapunov dimensions of invariant measures $mu$ for which $intPhi,dmu=alpha$. Our multifractal results are new in both the finitely generated and the infinitely generated setting." @default.
• W2039148753 created "2016-06-24" @default.
• W2039148753 creator A5014745514 @default.
• W2039148753 creator A5064091476 @default.
• W2039148753 date "2014-01-01" @default.
• W2039148753 modified "2023-09-24" @default.
• W2039148753 title "Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets" @default.
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• W2039148753 doi "https://doi.org/10.4171/jfg/3" @default.
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