Proves existence of trajectories asymptotic to formal invariant curves for C^∞ vector fields in R^m when the Taylor expansion is non-zero along the curve, plus an invariant C^0 manifold of such trajectories and non-oscillating behavior in the analytic case.
Solutions of definable ODEs with regular separation and dichotomy interlacement versus Hardy
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Trajectories of vector fields asymptotic to formal invariant curves
Proves existence of trajectories asymptotic to formal invariant curves for C^∞ vector fields in R^m when the Taylor expansion is non-zero along the curve, plus an invariant C^0 manifold of such trajectories and non-oscillating behavior in the analytic case.