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Period function of planar turning points

Journal Contribution - Journal Article

This paper is devoted to the study of the period function of planar generic and non-generic turning points. In the generic case (resp. non-generic) a non-degenerate (resp. degenerate) center disappears in the limit ϵ→0, where ϵ≥0 is the singular perturbation parameter. We show that, for each ϵ>0 and ϵ∼0, the period function is monotonously increasing (resp. has exactly one minimum). The result is valid in an ϵ-uniform neighborhood of the turning points. We also solve a part of the conjecture about a uniform upper bound for the number of critical periods inside classical Liénard systems of fixed degree, formulated by De Maesschalck and Dumortier in 2007. We use singular perturbation theory and the family blow-up.
Journal: Electronic Journal of Qualitative Theory of Differential Equations
ISSN: 1417-3875
Issue: 16
Pages: 1 - 21
Publication year:2021
Keywords:critical periods, family blow-up, period function, slow-fast systems
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:1
Authors:International
Authors from:Higher Education
Accessibility:Open