Orbitally symmetric systems with applications to planar centers

<p style='text-indent:20px;'>We present a generalization of the most usual symmetries in differential equations known as time-reversibility and equivariance ones. We check that typical properties are also valid for new definition unifies both. With it, we able to families planar polynomial vector fields having equilibrium points center type. Moreover, provide highest lower bound local cyclicity an point degree 6, <inline-formula><tex-math id="M1">\begin{document}$ M(6)\ge 48. $\end{document}</tex-math></inline-formula></p>