Global Saddles for Planar Maps
  We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of $D_2$-symmetric maps, for which we obtain a similar result for $C^1$ homeomorphisms. Some applications to differential equations are also given. 
Bego\~na Alarc\'on, Sofia B.S.D. Castro and Isabel S. Labouriau
math.DS