Piecewise holomorphic systems

Gabriel Rondon
Data do Evento: 
sexta-feira, 07 de Junho de 2024 - 10:00
Local do evento
Sala 321


Title: Piecewise holomorphic systems

Abstract:   Holomorphic systems are well known in the literature due to their important properties: reversibility, integrability, non-existence of limit cycles and complete knowledge of the phase portraits around their non-essential singularities.  In this work we are concerned with determining the number of limit cycles for piecewise holomorphic systems with a straight line of discontinuity. For that, we give the general formulas to calculate the Lyapunov quantities for these types of systems and we use these quantities to generate limit cycles for the focus-focus case. Also, the averaging method is employed to study bounds of limit cycles in the center-center case. In addition, we provide sufficient conditions to ensure that piecewise linear holomorphic systems have at least 3 limit cycles bifurcating from the infinity. Finally, we give families of this class of systems that possess algebraic limit cycles.