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- W1989294404 abstract "Let Fq be a finite field with q elements and Fq((X−1)) be the field of the formal Laurent series with an indeterminant X. Let Tβ be the β-transformation defined on Fq((X−1)). This paper is concerned with the size of the following dynamically defined limsup set{x∈Fq((X−1)):‖Tβnx−y0‖<q−(f(x)+⋯+f(Tβn−1x)),for infinitely manyn∈N}, for any given y0∈Fq((X−1)), where f is a positive continuous function and ‖⋅‖ is the norm, defined on Fq((X−1)). We show that its Hausdorff dimension is given as the solution s0 to the pressure function equationP(−s(degβ+f),Tβ)=0." @default.
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- W1989294404 date "2015-07-01" @default.
- W1989294404 modified "2023-10-14" @default.
- W1989294404 title "Dynamical Diophantine approximation of beta expansions of formal Laurent series" @default.
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- W1989294404 doi "https://doi.org/10.1016/j.ffa.2015.01.011" @default.
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