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Additional title: | On the number of limit cycles of the differential equations |
Date: | 2015 |
Abstract: | The notion of Hilbert number from polynomial differential systems in the plane of degree n can be extended to the differential equations of the form dr/dθ = a(θ) /∑n j=0 aj (θ)r j (∗) defined in the region of the cylinder where ∑n j=0 aj (θ)r j ̸= 0 as follows. The Hilbert number H(n) is the supremum of the number of limit cycles that any differential equation (*) on the cylinder of degree n in the variable r can have. We prove that H(n) = ∞ for all n ≥ 1. |
Grants: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410 European Commission 316338 European Commission 318999 |
Note: | El títol de la versió pre-print de l'article és: On the number of limit cycles of the differential equations |
Note: | Agraïments: FEDER-UNAB-10-4E-378 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Averaging theory ; Hilbert number ; Periodic orbit ; Trigonometric polynomial |
Published in: | Journal of Applied Analysis and Computation, Vol. 5 Núm. 1 (2015) , p. 141-145, ISSN 2158-5644 |
Postprint 6 p, 614.7 KB |