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Normal forms of Liénard type for analytic unfoldings of nilpotent singularities

Author: Renato Huzak
Journal: Proc. Amer. Math. Soc. 145 (2017), 4325-4336
MSC (2010): Primary 37G05; Secondary 34M45
Published electronically: March 27, 2017
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Abstract: Using the technique of gluing complex manifolds (equipped with vector fields) developed by Loray and the theory of deformation of complex structures developed by Kodaira and Spencer, we find normal forms of Liénard type for analytic unfoldings of planar singularities with a nonradial linear part. In particular, we improve normal forms of Takens for analytic unfoldings of nilpotent singularities and normal forms of De Maesschalck, Dumortier and Roussarie for analytic unfoldings of nilpotent contact points in planar slow-fast systems.

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Additional Information

Renato Huzak
Affiliation: Hasselt University, Campus Diepenbeek, Agoralaan Gebouw D, 3590 Diepenbeek, Belgium

Received by editor(s): June 20, 2016
Received by editor(s) in revised form: October 17, 2016
Published electronically: March 27, 2017
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society

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