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Critical periods in planar polynomial centers near a maximum number of cusps.
- Source :
-
Journal of Differential Equations . Jan2024, Vol. 380, p181-197. 17p. - Publication Year :
- 2024
-
Abstract
- We 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 n 2 − 2 (resp. n 2 − 2 n − 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *VECTOR fields
*POLYNOMIALS
*CUSP forms (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 380
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 173888087
- Full Text :
- https://doi.org/10.1016/j.jde.2023.10.034