Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithm laws for equilibrium states in negative curvature   Let $M$ be a pinched negatively curved Riemannian manifold, whose unit
tangent bundle is endowed with a Gibbs measure $m_F$ associated to a potential
$F$. We compute the Hausdorff dimension of the conditional measures of $m_F$.
We study the $m_F$-almost sure asymptotic penetration behaviour of locally
geodesic lines of $M$ into small neighbourhoods of closed geodesics, and of
other compact (locally) convex subsets of $M$. We prove Khintchine-type and
logarithm law-type results for the spiraling of geodesic lines around these
objects. As an arithmetic consequence, we give almost sure Diophantine
approximation results of real numbers by quadratic irrationals with respect to
general H\"older quasi-invariant measures.

9
The categories of this paper are: nlin
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat