Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On natural invariant measures on generalised iterated function systems   We consider the limit set of generalised iterated function systems. Under the
assumption of a natural potential, the so called cylinder function, we prove
the existence of the invariant probability measure satisfying the equilibrium
state. We motivate this approach by showing that for typical self-affine sets
there exists an ergodic invariant measure having the same Hausdorff dimension
as the set itself.

6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat