RT Journal Article
T1 The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line
A1 Esteban, Marina
A1 Llibre, Jaume
A1 Valls, Claudia
K1 Limit Cycles
K1 Discontinuous System
K1 Isochronous center
AB In this paper, we deal with discontinuous piecewise differential systems formed by two differential systems separated by a straight line when these two differential systems are linear centers (which always are isochronous) or quadratic isochronous centers. It is known that there is a unique family of linear isochronous centers and four families of quadratic isochronous centers. Combining these five types of isochronous centers, we obtain 15 classes of discontinuous piecewise differential systems. We provide upper bounds for the maximum number of limit cycles that these fifteen classes of discontinuous piecewise differential systems can exhibit, so we have solved the 16th Hilbert problem for such differential systems. Moreover, in seven of the classes of these discontinuous piecewise differential systems, the obtained upper bound on the maximum number of limit cycles is reached.
PB AIP Publishing
YR 2021
FD 2021-04-07
LK https://hdl.handle.net/10433/22245
UL https://hdl.handle.net/10433/22245
LA en
NO Chaos 31, 043112 (2021)
NO Departamento de Economía, Métodos Cuantitativos e Historia Económica. Universidad Pablo de Olavide.
DS RIO
RD Apr 23, 2026