New dynamical features of pure k-essential cosmologies

We come back on the dynamical properties of k-essential cosmological models and show how interesting phenomenological features those are related to existence boundaries in phase surface. focus our attention branching points where energy density has an extremum effective speed sound diverges. discuss behaviour solutions a general class exhibiting such curves give two possible interpretations; most possibility regards arrow time that is reversed trespassing curve. This study teaches us something new about FLRW cosmologies fluids driving cosmic evolution have equations state multivalued functions other thermodynamical quantities.