The Hilbert number of a class of differential equations
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Makhlouf, Ammar (UBMA University Annaba (Algeria). Department of mathematics)

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

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles