| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Estadual Paulista, Math Dept, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[2] Univ Autonoma Barcelona, Dept Matemat, Edif Cc, E-08193 Barcelona - Spain
[3] Ctr Recerca Matemat, Edif Cc, Campus Bellaterra, Barcelona 08193 - Spain
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 207, JUN 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
We apply the averaging method in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our results can be applied to models where the smoothness is lost on the set Sigma = [xy = 0]. They also motivate to consider a variant of Hilbert 16th problem, where the goal is to bound the number of limit cycles in terms of the number of monomials of a family of polynomial vector fields, instead of doing this in terms of their degrees. (C) 2021 Elsevier Ltd. All rights reserved. (AU) | |
| FAPESP's process: | 16/00242-2 - Bifurcation of piecewise smooth systems with singular borders via regularization |
| Grantee: | Yagor Romano Carvalho |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 18/05098-2 - Study of limit cycles in piecewise smooth systems on the cylinder |
| Grantee: | Yagor Romano Carvalho |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |