Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graph-directed systems and self-similar measures on limit spaces of
  self-similar groups   Let $G$ be a group and $\phi:H\to G$ be a contracting homomorphism from a
subgroup $H<G$ of finite index. V.Nekrashevych [25] associated with the pair
$(G,\phi)$ the limit dynamical system $(\lims,\si)$ and the limit $G$-space
$\limGs$ together with the covering $\cup_{g\in G}\tile\cdot g$ by the tile
$\tile$. We develop the theory of self-similar measures $\mu$ on these limit
spaces. It is shown that $(\lims,\si,\mu)$ is conjugated to the one-sided
Bernoulli shift. Using sofic subshifts we prove that the tile $\tile$ has
integer measure and we give an algorithmic way to compute it. In addition we
give an algorithm to find the measure of the intersection of tiles $\tile\cap
(\tile\cdot g)$ for $g\in G$. We present applications to the invariant measures
for the rational functions on the Riemann sphere and to the evaluation of the
Lebesgue measure of integral self-affine tiles.

27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg