The Dulac map near a normally hyperbolic manifold of saddle singularities is shown to admit an asymptotic expansion built from the Ecalle-Roussarie compensator, generalizing the planar saddle result.
Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three
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Normal Forms for Manifolds of Normally Hyperbolic Singularities and Asymptotic Properties of Nearby Transitions
The Dulac map near a normally hyperbolic manifold of saddle singularities is shown to admit an asymptotic expansion built from the Ecalle-Roussarie compensator, generalizing the planar saddle result.