Limit Cycles of Planar Discontinuous Piecewise Linear Hamiltonian Systems Without Equilibria Separated by Nonregular Curves

Autor:	Jimenez, Johana, Llibre, Jaume, Valls, Clàudia
Rok vydání:	2022
Předmět:	Nonregular curve Applied Mathematics Modeling and Simulation Crossing limit cycle Engineering (miscellaneous) Discontinuous piecewise linear Hamiltonian system
Zdroj:	International Journal of Bifurcation and Chaos. 32
ISSN:	1793-6551 0218-1274
DOI:	10.1142/s021812742250184x
Popis:	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 [Formula: see text] 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f808c6cfef3ec9e60ab6cf6f39a7ba09 https://doi.org/10.1142/s021812742250184x Zobrazit plný text záznamu