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Title: | Critical periods in planar polynomial centers near a maximum number of cusps | Authors: | DE MAESSCHALCK, Peter Torregrosa, Joan |
Issue Date: | 2024 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | Journal of Differential Equations, 380 , p. 181 -197 | Abstract: | provide the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. This lower bound doubles the previous one from the literature, and we end up with at least n2 - 2 (resp. n2 - 2n - 1) critical periods for planar polynomial systems of odd (resp. even) degree n. Key idea is the perturbation of a vector field with many cusp equilibria, whose construction is by itself a nontrivial construction that uses elements of catastrophe theory.(c) 2023 Elsevier Inc. All rights reserved. | Notes: | De Maesschalck, P (corresponding author), Hasselt Univ, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium. peter.demaesschalck@uhasselt.be; joan.torregrosa@uab.cat |
Keywords: | Critical periods;Hamiltonian vector fields;Best lower bound;Degree n vector field | Document URI: | http://hdl.handle.net/1942/41982 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2023.10.034 | ISI #: | 001110106000001 | Rights: | 2023 Elsevier Inc. All rights reserved. | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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Critical periods in planar polynomial centers near a maximum number of cusps.pdf Restricted Access | Published version | 372.29 kB | Adobe PDF | View/Open Request a copy |
DeMTor2023.pdf | Peer-reviewed author version | 647.65 kB | Adobe PDF | View/Open |
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