New lower bound for the Hilbert number in piecewise quadratic differential systems

By L. P. D. da Cruz, Douglas Duarte Novaes, Joan Torregrosa. Journal of Differential Equations, 2018

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Abstract 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 H p ( n ) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then H p ( 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.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/aeffd1c4ec027514f31f98623dc542a2ad11c66a