{"id":"palomar/PALOMAR-2026-10-22-000008","url":"https://github.com/mmislan/palomar-lienard-limit-cycles/tree/7da225327c6cd62a3dc63926525377764ea8f454","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-22-000008-v1.json","repo":"https://github.com/mmislan/palomar-lienard-limit-cycles","tags":["math.DS","msc:34C07","msc:34C25","msc:68V15","dynamical-systems","limit-cycles","ordinary-differential-equations"],"score":0,"title":"Classical Liénard equations of degree n ≥ 6 can have floor((n−1)/2)+4 limit cycles","trust":"high","domain":"math.DS","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-22","reactions":{},"formalized":true,"formalizes":[{"title":"Classical Liénard equations of degree n ≥ 6 can have floor((n−1)/2)+4 limit cycles","identifier":"sha256:5db329356367f4b2f99c903d73c0eddd9abdd8845c623a94277cac2b8a96347b","relationship":"formalizes"},{"title":"OpenAI math: polynomial local-flow prefix in SmoothFlow.lean","identifier":"git:fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","relationship":"adapts"}]}