  In this article we describe the construction of logarithmic models for germs
of plane singular analytic foliations, both real and complex. A logarithmic
model is a germ of closed meromorphic 1-form with simple poles produced upon
some specified geometric data: the structure of dicritical (non-invariant)
components in the exceptional divisor of its reduction of singularities, a
prescribed finite set of separatrices - invariant analytic branches at the
origin - and Camacho-Sad indices with respect to these separatrices. As an
application, we use logarithmic models in order to construct real and complex
germs of meromorphic functions with a given indeterminacy structure and
prescribed sets of zeroes and poles. Also, in the real case, logarithmic models
are used in order to build germs of analytic vector fields with a given
Bendixson's sectorial decomposition of a neighborhood of $0 \in \mathbb{R}^{2}$
into hyperbolic, parabolic and elliptic sectors. This is carried out in the
specific case where all trajectories accumulating to the origin are contained
in analytic curves. As a consequence, we can produce real meromorphic functions
with a prescribed sectorial decomposition.
