Normal form power series for reducible analytic submanifolds under eventually free Lie pseudo-group actions converge whenever the moving-frame cross-section is well-posed and analytic.
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Convergence of Normal Form Power Series for Infinite-Dimensional Lie Pseudo-Group Actions
Normal form power series for reducible analytic submanifolds under eventually free Lie pseudo-group actions converge whenever the moving-frame cross-section is well-posed and analytic.