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

被引：0

作者：

Jimenez, Johana ^{[1
]}

Llibre, Jaume ^{[2
]}

Valls, Claudia ^{[3
]}

机构：

[1] Univ Fed Oeste Bahia, BR-47600000 Bom Jesus Da Lapa, BA, Brazil

[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain

[3] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon, Portugal

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2022年 / 32卷 / 12期

基金：

欧盟地平线“2020”;

关键词：

Crossing limit cycle; discontinuous piecewise linear Hamiltonian system; nonregular curve; GLOBAL PROPERTIES; VECTOR-FIELDS;

D O I：

10.1142/S021812742250184X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 R-2 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.

引用

页数：23

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