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Dulac maps of real saddle-nodes

Nonlinearity. 2024. Vol. 37. No. 10. Article 105017.
Ilyashenko Y.

Consider a germ of a holomorphic vector field at the origin on the coordinate complex plane. This germ is called a saddle-node if the origin is its singular point, one of its eigenvalues at zero is zero, and the other is not. A saddle-node germ is real if its restriction to the real plane is real. The monodromy transformation for this germ has a multiplier at zero equal to 1. The germ of this map is parabolic and admits a ‘normalizing cochain’. In this note we express the Dulac map of any real saddle-node up to a left composition with a real germ (C, 0)→(C, 0) through one component of the cochain normalizing the monodromy transformation.

Research target: Mathematics
Language: English
Full text
DOI
Keywords: monodromymodulisaddle-nodeecalle-voroninmartinet-ramis
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