  This paper deals with the existence of $N$ vortex patches located at the
vertex of a regular polygon with $N$ sides that rotate around the center of the
polygon at a constant angular velocity. That is done for Euler and
(SQG)$_\beta$ equations, with $\beta\in(0,1)$, but may be also extended to more
general models. The idea is the desingularization of the Thomsom polygon for
the $N$ point vortex system, that is, $N$ point vortices located at the vertex
of a regular polygon with $N$ sides. The proof is based on the study of the
contour dynamics equation combined with the application of the infinite
dimensional Implicit Function theorem and the well--chosen of the function
spaces.
