RT Journal Article
T1 Complex normal forms for planar double boundary focus points
A1 Esteban, Marina
A1 Freire, Emilio
A1 Ponce, Enrique
A1 Torres, Francisco
K1 Piecewise smooth systems
K1 Normal forms
K1 Pseudo-focus
AB We consider planar piecewise smooth systems constituted by two vector fields with a straight line as separation boundary between them. It is assumed that the origin, which belongs to the boundary, is an isolated equilibrium of center-focus type for both vector fields. Working in the complex setting, firstly we obtain a general normal form with only one term for each degree. Next, we exploit such a normal form, which turns to be very suitable for computing the Lyapunov constants that characterize the cyclicity of the origin. To illustrate the usefulness of the approach, some significative examples regarding piecewise quadratic Liénard systems are considered. In particular, we show how a piecewise quadratic system with an attractive weak focus from both sides can give rise to a repulsive weak focus.
PB Elsevier
YR 2025
FD 2025-07-04
LK https://hdl.handle.net/10433/24840
UL https://hdl.handle.net/10433/24840
LA en
NO Departamento de Economía, Métodos Cuantitativos e Historia Económica
DS RIO
RD May 8, 2026