The 16th Hilbert Problem for Discontinuous Piecewise Linear Hamiltonian Saddles and Isochronous Centers Separated by a Straight Line
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Date:	2024
Abstract:	We provide the maximum number of limit cycles for discontinuous piecewise differential systems separated by a straight line and formed by a linear Hamiltonian saddle and one of the four families of quadratic isochronous centers. Hence we have solved the extension of the 16th Hilbert problem to such piecewise differential systems and for two of these four classes of discontinuous piecewise differential systems the obtained upper bound for the maximum number of limit cycles is reached.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-100 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Discontinuous piecewise linear differential systems ; Linear Hamiltonian saddles ; Limit cycles ; Isochronous center
Published in:	Differential Equations and Dynamical Systems, (May 2024) , ISSN 0974-6870

DOI: 10.1007/s12591-024-00695-w

Postprint 10 p, 579.0 KB

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