Publicación: CROSSING LIMIT CYCLES FOR DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL CENTERS SEPARATED BY THREE PARALLEL STRAIGHT LINES
Fecha
2023
Título de la revista
ISSN de la revista
Título del volumen
Editor
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO SERIES
Resumen
IN THIS PAPER WE STUDY THE CONTINUOUS AND DISCONTINUOUS PLANAR PIECEWISE DIFFERENTIAL SYSTEMS FORMED BY FOUR LINEAR CENTERS SEPARATED BY THREE PARALLEL STRAIGHT LINES DENOTED BY ?={(X,Y)?R2:X=?P,X=0,X=Q, P,Q>0}. WE PROVE THAT WHEN THESE PIECEWISE DIFFERENTIAL SYSTEMS ARE CONTINUOUS THEY HAVE NO LIMIT CYCLES. WHILE FOR THE DISCONTINUOUS CASE WE SHOW THAT THEY CAN HAVE AT MOST FOUR LIMIT CYCLES AND WE ALSO PROVIDE EXAMPLES OF SUCH SYSTEMS WITH ZERO, ONE, AND TWO LIMIT CYCLES. IN PARTICULAR WE HAVE SOLVED THE EXTENSION OF THE 16TH HILBERT PROBLEM TO THIS CLASS OF PIECEWISE DIFFERENTIAL SYSTEMS.
Descripción
Palabras clave
Linear centers, Limit cycles, First integrals, Discontinuous piecewise differential systems, Continuous piecewise differential systems
