  We investigate static spherically symmetric perfect fluid models in Newtonian
gravity for barotropic equations of state that are asymptotically polytropic at
low and high pressures. This is done by casting the equations into a
3-dimensional regular dynamical system with bounded dependent variables. The
low and high central pressure limits correspond to two 2-dimensional boundary
subsets, described by homology invariant equations for exact polytropes. Thus
the formulation naturally places work about polytropes in a more general
context. The introduced framework yields a visual aid for obtaining qualitative
information about the solution space and is also suitable for numerical
investigations. Last, but not least, it makes a host of mathematical tools from
dynamical systems theory available. This allows us to prove a number of
theorems about the relationship between the equation of state and properties
concerning total masses and radii.
