This paper presents aštopological approach tošthe search and stability analysis ofšrelative equilibria ofšthree point vortices ofšequal intensities. Itšisšshown that the equations ofšmotion can bešreduced byšone degree ofšfreedom. Wešhave found two new stationary configurations (isosceles and non-symmetrical collinear) and studied their bifurcations and stability.

With the help ofšmathematical modelling, wešstudy the dynamics ofšmany point vortices system onšthe plane. For this system, wešconsider the following cases:
?švortex rings with outer radius $r = 1$šand variable inner radius $r_0$,
?švortex ellipses with semiaxesš$a$, $b$.
The emphasis isšonšthe analysis ofšthe asymptotic $(t ? ?)$ behavior ofšthe system and onšthe verification ofšthe stability criteria for vorticity continuous distributions.