Global Saddles for Planar Maps

Abstract

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.

References in corpus (1)

• Rotation numbers for planar attractors of equivariant homeomorphisms