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Global saddles for planar maps. (English) Zbl 1394.37049

Summary: 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.

MSC:

37C75 Stability theory for smooth dynamical systems
37C80 Symmetries, equivariant dynamical systems (MSC2010)
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37C20 Generic properties, structural stability of dynamical systems
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
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References:

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