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Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three. (English) Zbl 1017.37009
Summary: We study the Dulac map associated to a vector field defined in a neighborhood of a hyperbolic equilibrium point of saddle type i.e. the map from a section transverse to the 2-dimensional stable manifold to another section transverse to the unstable one. We give an asymptotic expression of this Dulac map. We show that, this asymptotic expression has the same expression, up to some multiplication by a function of Mourtada type, as in the case where the vector field is linear.
##### MSC:
 37C10 Vector fields, flows, ordinary differential equations 37C75 Stability theory 37D05 Hyperbolic orbits and sets