{"id":"openai-math/two-limit-cycles-for-quintic-lienard-systems","pdf":"https://github.com/openai/math/blob/main/preprints/two-limit-cycles-for-quintic-lienard-systems-September-24-2026/two-limit-cycles-for-quintic-lienard-systems-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/two-limit-cycles-for-quintic-lienard-systems-September-24-2026","tags":["dynamical-systems","limit-cycles","lienard-systems","polynomial-vector-fields"],"score":0,"title":"Two limit cycles for quintic Liénard systems","domain":"Dynamical systems and ergodic theory","family":"143","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DS","summary":"Every classical Liénard system $`\\dot x=y-F(x)`$, $`\\dot y=-x`$, with F an arbitrary real polynomial of degree at most five, has at most two geometrically distinct isolated periodic orbits, and the bound is attained. This proves the degree-five case of the Lins Neto–de Melo–Pugh conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Hilbert's sixteenth problem: uniform bounds for limit cycles"}