Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization dimension for Gibbs-like measures on cookie-cutter sets   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 $r\in (0, +\infty)$
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.

3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn