Germs of non-dicritical and dicritical foliation pairs with degenerate singularities have their tangency curves fully described via k-normal forms of normalizing transformations, with a realization theorem showing generic transversal analytic curves arise this way.
Œuvres, tome I, pp
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Curves of tangencies of foliation pairs and normalizing transformations
Germs of non-dicritical and dicritical foliation pairs with degenerate singularities have their tangency curves fully described via k-normal forms of normalizing transformations, with a realization theorem showing generic transversal analytic curves arise this way.