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http://hdl.handle.net/1942/33818
Title: | Period function of planar turning points | Authors: | HUZAK, Renato Rojas, David |
Issue Date: | 2021 | Publisher: | Source: | Electronic Journal of Qualitative Theory of Differential Equations, (16) , p. 1 -21 | Abstract: | 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. | Keywords: | critical periods;family blow-up;period function;slow-fast systems | Document URI: | http://hdl.handle.net/1942/33818 | ISSN: | 1417-3875 | e-ISSN: | 1417-3875 | DOI: | 10.14232/ejqtde.2021.1.16 | ISI #: | WOS:000636063100001 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
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p8850.pdf | Published version | 946.38 kB | Adobe PDF | View/Open |
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