Dynamics of classes of barotropic fluids in spatially curved FRW spacetimes

In this article we perform dynamical analysis of a broad class of barotropic fluids in the spatially curved Friedmann-Robertson-Walker (FRW) spacetime background without considering the cosmological constant. The first part of our study concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS) having as the only assumption the non-negativity of the fluid's energy density. After defining a new set of dimensionless variables and a new evolution parameter, we introduce the function Gamma that encodes the EoS. In this general setup several features of the system are identified: critical points, invariant subsets and the characteristics of the function Gamma, along with their cosmological interpretations. The second part of our work provides two examples with specific Gamma functions. In the first example we provide a Gamma function and then we exhibit how it can be trimmed down to a specific class of EoS through physical arguments, while in the second example we discuss the quadratic EoS studied in Phys. Rev. D 74, 023523 (2006) by comparing our approach with their analysis.