Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by nonregular curves
Jimenez, Johana (Universidade Federal do Oeste da Bahia (Brazil))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)

Data:	2022
Resum:	The problem of determining the existence, maximum number and positions of the limit cycles of the planar discontinuous piecewise linear differential systems is an important problem in the qualitative theory of differential systems. In this paper, we study two families of piecewise linear Hamiltonian systems without equilibria in ℝ2 separated by a nonregular curve. We provide the maximum number of crossing limit cycles that each family can have and show when this maximum is reached. In this way we are solving for each family the extended 16th Hilbert problem.
Ajuts:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Crossing limit cycle ; Discontinuous piecewise linear Hamiltonian system ; Nonregular curve
Publicat a:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 12 (September 2022) , art. 2250184, ISSN 1793-6551

DOI: 10.1142/S021812742250184X

Postprint 16 p, 458.9 KB

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