Classical Liénard equations of degree n ≥ 6 can have floor((n−1)/2)+4 limit cycles
For the classical Liénard system dx/dt = y − F(x), dy/dt = −x, every polynomial in an explicit coefficient box of radius 10^−40 around a rational sextic has at least six limit cycles. For every integer n ≥ 6, a real polynomial of degree exactly n with F(0) = 0 is shown to have at least floor((n − 1)/2) + 4 limit cycles. An explicit rational polynomial of degree seven, obtained by adding 10^−41 x^7 to the sextic, has at least seven limit cycles. The conclusions provide global nonconstant periodic solutions with pairwise disjoint images, prescribed positive-axis crossings and isolating…
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