Home > Articles > Published articles > The 16th Hilbert problem restricted to circular algebraic limit cycles |
Date: | 2016 |
Abstract: | We prove the following two results. First every planar polynomial vector field of degree S with S invariant circles is Darboux integrable without limit cycles. Second a planar polynomial vector field of degree S admits at most S - 1 invariant circles which are algebraic limit cycles. In particular we solve the 16th Hilbert problem restricted to algebraic limit cycles given by circles, because a planar polynomial vector field of degree S has at most S - 1 algebraic limit cycles given by circles, and this number is reached. |
Grants: | Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad TSI2007-65406-C03-01 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338 |
Note: | Agraïments: FEDER-UNAB10-4E-378 and Consolider CSD2007-00004 "ES" |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Darboux integrability ; Invariant algebraic circles ; Planar polynomial differential system ; Polynomial vector fields |
Published in: | Journal of differential equations, Vol. 260 (2016) , p. 5726-5760, ISSN 1090-2732 |
Postprint 32 p, 789.9 KB |