Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On self-affine measures with equal Hausdorff and Lyapunov dimensions   Let $\mu$ be a self-affine measure on $\mathbb{R}^{d}$ associated to a
self-affine IFS $\{\varphi_{\lambda}(x) = A_{\lambda}x +
v_{\lambda}\}_{\lambda\in\Lambda}$ and a probability vector
$p=(p_{\lambda})_{\lambda}>0$. Assume the strong separation condition holds.
Let $\gamma_{1}\ge...\ge\gamma_{d}$ and $D$ be the Lyapunov exponents and
dimension corresponding to $\{A_{\lambda}\}_{\lambda\in\Lambda}$ and
$p^{\mathbb{N}}$, and let $\mathbf{G}$ be the group generated by
$\{A_{\lambda}\}_{\lambda\in\Lambda}$. We show that if
$\gamma_{m+1}>\gamma_{m}=...=\gamma_{d}$, if $\mathbf{G}$ acts irreducibly on
the vector space of alternating $m$-forms, and if the Furstenberg measure
$\mu_{F}$ satisfies $\dim_{H}\mu_{F}+D>(m+1)(d-m)$, then $\mu$ is exact
dimensional with $\dim\mu=D$.

14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys