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• W2899525890 abstract "Abstract We study L q -spectra of planar self-affine measures generated by diagonal matrices. We introduce a new technique for constructing and understanding examples based on combinatorial estimates for the exponential growth of certain split binomial sums. Using this approach we disprove a theorem of Falconer and Miao from 2007 and a conjecture of Miao from 2008 concerning a closed form expression for the generalised dimensions of generic self-affine measures. We also answer a question of Fraser from 2016 in the negative by proving that a certain natural closed form expression does not generally give the L q -spectrum. As a further application we provide examples of self-affine measures whose L q -spectra exhibit new types of phase transitions. Finally, we provide new non-trivial closed form bounds for the L q -spectra, which in certain cases yield sharp results." @default.
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• W2899525890 date "2021-08-02" @default.
• W2899525890 modified "2023-10-17" @default.
• W2899525890 title "L ^q-spectra of self-affine measures: closed forms, counterexamples, and split binomial sums" @default.
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• W2899525890 doi "https://doi.org/10.1088/1361-6544/ac14a2" @default.
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