Limit cycles for some families of smooth and non-smooth planar systems
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 Σ = {xy = 0}. They also...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:239781 |
| Online Access: | https://ddd.uab.cat/record/239781 https://dx.doi.org/urn:doi:10.1016/j.na.2021.112298 |
| Access Level: | Open access |
| Keyword: | Limit cycles First order averaging Extended complete Chebyshev systems Hilbert numbers |
| Summary: | 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 Σ = {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. |
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