The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y= xn
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Date:	2023
Abstract:	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.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2022/SGR-00113 European Commission 777911
Note:	Altres ajuts: Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Non-smooth differential system ; Limit cycle ; Discontinuous piecewise linear differential system ; Linear centers ; Linear Hamiltonian saddles
Published in:	Mathematical Physics, Analysis and Geometry, Vol. 26, Issue 4 (December 2023) , art. 25, ISSN 1572-9656

DOI: 10.1007/s11040-023-09467-4

Postprint 10 p, 347.6 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles