Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Thermodynamical Formalism and Real Analyticity for Meromorphic
  Functions of Finite Order   Working with well chosen Riemannian metrics and employing Nevanlinna's
theory, we make the thermodynamical formalism work for a wide class of
hyperbolic meromorphic functions of finite order (including in particular
exponential family, elliptic functions, cosine, tangent and the cosine--root
family and also compositions of these functions with arbitrary polynomials). In
particular, the existence of conformal (Gibbs) measures is established and then
the existence of probability invariant measures equivalent to conformal
measures is proven. As a geometric consequence of the developed thermodynamic
formalism, a version of Bowen's formula expressing the Hausdorff dimension of
the radial Julia set as the zero of the pressure function and, moreover, the
real analyticity of this dimension, is proved.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat