{"id":"palomar/PALOMAR-2026-09-22-000001","url":"https://github.com/MColbrook/Eden_conjecture/tree/9e803e9885d23064a24b138b0068a249f97d13ed","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-22-000001-v1.json","repo":"https://github.com/MColbrook/Eden_conjecture","tags":["math.DS","msc:37C45","msc:37D25","msc:34D45","dynamical-systems","attractors","lyapunov-dimension"],"score":0,"title":"A counterexample to the unrestricted form of Eden's conjecture","trust":"high","domain":"math.DS","source":"palomar","authors":["Matthew J. Colbrook"],"reviews":0,"subject":"math.DS","summary":"For every c > 4, an explicit polynomial ODE on Euclidean five-space has a compact global attractor and uniformly negative divergence. Its finite-time local Lyapunov dimension at every positive real time and its asymptotic Kaplan--Yorke dimension have maximum 4 + 4/c, attained precisely on an invariant two-torus with irrational angular flow. The maximum over equilibria and periodic points is 3. All singular-value exponents exist, and local dimensions converge pointwise. This disproves the unrestricted form of Eden's conjecture; the attractor is not assumed transitive.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-22","reactions":{},"formalized":true,"formalizes":[{"title":"Aperiodic maximisers of Lyapunov dimension: A counterexample to the unrestricted form of Eden's conjecture","identifier":"https://doi.org/10.5281/zenodo.22883032","relationship":"formalizes"}]}