TY - JOUR
T1 - New lower bound for the Hilbert number in piecewise quadratic differential systems
AU - da Cruz, Leonardo P.C.
AU - Novaes, Douglas D.
AU - Torregrosa, Joan
PY - 2019/3/15
Y1 - 2019/3/15
N2 - © 2018 Elsevier Inc. We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by Hp(n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then Hp(2)≥16. As fas as we are concerned, this is the best lower bound for the quadratic class. Moreover, in the studied cases, all limit cycles appear nested bifurcating from a period annulus of a isochronous quadratic center.
AB - © 2018 Elsevier Inc. We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by Hp(n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then Hp(2)≥16. As fas as we are concerned, this is the best lower bound for the quadratic class. Moreover, in the studied cases, all limit cycles appear nested bifurcating from a period annulus of a isochronous quadratic center.
KW - First and second order perturbations of isochronous quadratic systems
KW - Hilbert number for piecewise quadratic differential systems
KW - Limit cycles in piecewise quadratic differential systems
KW - Non-smooth differential system
UR - http://www.mendeley.com/research/new-lower-bound-hilbert-number-piecewise-quadratic-differential-systems
U2 - 10.1016/j.jde.2018.09.032
DO - 10.1016/j.jde.2018.09.032
M3 - Article
SN - 0022-0396
VL - 266
SP - 4170
EP - 4203
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -