The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y= xn
We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in t...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:299284 |
| Online Access: | https://ddd.uab.cat/record/299284 https://dx.doi.org/urn:doi:10.1007/s11040-023-09467-4 |
| Access Level: | Open access |
| Keyword: | Non-smooth differential system Limit cycle Discontinuous piecewise linear differential system Linear centers Linear Hamiltonian saddles |
| Summary: | We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in terms of n, proving the extended 16th Hilbert problem in this case. In particular, we show that for n= 2 this bound can be reached. |
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