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- W4321153485 abstract "In this paper using Banach limit we have determined a Gibbs-like measure $mu_h$ supported by a cookie-cutter set $E$ which is generated by a single cookie-cutter mapping $f$. For such a measure $mu_h$ and $rin (0, +infty)$ we have shown that there exists a unique $kappa_r in (0, +infty)$ such that $kappa_r$ is the quantization dimension function of the probability measure $mu_h$, and established its functional relationship with the temperature function of the thermodynamic formalism. The temperature function is commonly used to perform the multifractal analysis, in our context of the measure $mu_h$. In addition, we have proved that the $kappa_r$-dimensional lower quantization coefficient of order $r$ of the probability measure is positive." @default.
- W4321153485 created "2023-02-18" @default.
- W4321153485 creator A5006255270 @default.
- W4321153485 date "2012-07-24" @default.
- W4321153485 modified "2023-09-29" @default.
- W4321153485 title "Quantization dimension for Gibbs-like measures on cookie-cutter sets" @default.
- W4321153485 doi "https://doi.org/10.48550/arxiv.1207.5842" @default.
- W4321153485 hasPublicationYear "2012" @default.
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