Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spiraling spectra of geodesic lines in negatively curved manifolds   Given a negatively curved geodesic metric space M, we study the asymptotic
penetration behaviour of geodesic lines of M in small neighbourhoods of closed
geodesics and of other compact convex subsets of M. We define a spiraling
spectrum which gives precise information on the asymptotic spiraling lengths of
geodesic lines around these objects. We prove analogs of the theorems of
Dirichlet, Hall and Cusick in this context. As a consequence, we obtain
Diophantine approximation results of real numbers, complex numbers, or elements
of the Heisenberg group by irrational quadratic ones.

6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th