Normal forms of Liénard type for analytic unfoldings of nilpotent singularities
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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.References
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Additional Information
- Renato Huzak
- Affiliation: Hasselt University, Campus Diepenbeek, Agoralaan Gebouw D, 3590 Diepenbeek, Belgium
- MR Author ID: 1035652
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4325-4336
- MSC (2010): Primary 37G05; Secondary 34M45
- DOI: https://doi.org/10.1090/proc/13539
- MathSciNet review: 3690616