Limit Cycles For M-piecewise Discontinuous Polynomial Liénard Differential Equations

We provide lower bounds for the maximum number of limit cycles for the m-piecewise discontinuous polynomial differential equations (Formula Precented.), (Formula Presented.), where the zero set of the function sgn(gm(x, y)) with m = 2, 4, 6,.. is the product of m/2 straight lines passing through the origin of coordinates dividing the plane into sectors of angle 2π/m, and sgn(z) denotes the sign function.

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