Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension of generic self-affine sets with holes   Let $(\Sigma, \sigma)$ be a dynamical system, and let $U\subset \Sigma$.
Consider the survivor set \[ \Sigma_U=\{x\in \Sigma\mid \sigma^n(x)\notin
U\textrm{for all}n\} \] of points that never enter the subset $U$. We study the
size of this set in the case when $\Sigma$ is the symbolic space associated to
a self-affine set $\Lambda$, calculating the dimension of the projection of
$\Sigma_U$ as a subset of $\Lambda$ and finding an asymptotic formula for the
dimension in terms of the K\"aenm\"aki measure of the hole as the hole shrinks
to a point. Our results hold when the set $U$ is a cylinder set in two cases:
when the matrices defining $\Lambda$ are diagonal, and when they are such that
the pressure is differentiable at its zero point, and the K\"aenm\"aki measure
is a strong-Gibbs measure.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th