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By means of N-body+Hydrodynamic zoom-in simulations we study the evolution ofthe inner dark matter and stellar mass distributions of central dwarf galaxiesformed in halos of virial masses Mv=2-3x10^10 Msun at z=0, both in a WDM andCDM cosmology. The half-mode mass in the WDM power spectrum of our simulationsis Mf= 2x 10^10 Msun. In the dark matter only simulations halo density profilesare well described by the NFW parametric fit in both cosmologies, though theWDM halos have concentrations lower by factors 1.5--2.0 than their CDMcounterparts. In the hydrodynamic simulations, the effects of baryonssignificantly flatten the inner density, velocity dispersion, and pseudophase-space density profiles of the WDM halos but not of the CDM ones. Thedensity slope measured at ~ 0.02xRv, alpha, becomes shallow in periods of 2 to5 Gyr in the WDM runs. We explore whether this flattening process correlateswith the global SF, Ms/Mv ratio, gas outflow, and internal specific angularmomentum histories. We do not find any clear trends but when alpha is shallowerthan -0.5, Ms/Mv is always between 0.25 and 1%. We conclude that the mainreason of the formation of the shallow core is the presence of strong gas massfluctuations inside the inner halo, which are a consequence of the feedbackdriven by a very bursty and sustained SF history in shallow gravitationalpotentials. Our WDM halos, which assemble late and are less concentrated thanthe CDM ones, obey these conditions. There are also (rare) CDM systems withextended mass assembly histories that obey these conditions and form indeedshallow cores. The dynamical heating and expansion processes, behind the DMcore flattening, apply also to the stars in a such a way that the stellar ageand metallicity gradients of the dwarfs are softened, their stellar half-massradii strongly grow with time, and their central surface densities decrease.

The inner structure of dwarf sized halos in Warm and Cold Dark Matter cosmologies