Existence of small loops in the Bifurcation diagram near the degenerate   eigenvalues
  In this paper we study for the incompressible Euler equations the global structure of the bifurcation diagram for the rotating doubly connected patches near the degenerate case. We show that the branches with the same symmetry merge forming a small loop provided that they are close enough. This confirms the numerical observations done in the recent work [10] 
Taoufik Hmidi, Coralie Renault
math.AP