Is the Feigenbaum delta constant transcendental?
TheoremDB P11200 · dynamical systems
Inferred from the community field; finer classification has not been reviewed.
Problem statement
For 0 <= mu <= 2, let (x)=1-mu*x^2. In its principal period-doubling cascade, let mu_n be the parameter at which the attracting cycle of least period 2^(n-1) has multiplier -1 and bifurcates to a cycle of period 2^n. Define delta=lim_{n->infinity}(mu_(n+1)-mu_n)/(mu_(n+2)-mu_(n+1)), the Feigenbaum delta constant. Is delta transcendental over the rational numbers?
Lean 4
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Background
Additional formulation recorded by the source
f_\mu(x)=1-\mu x^2,\quad \delta=\lim_{n\to\infty}\frac{\mu_{n+1}-\mu_n}{\mu_{n+2}-\mu_{n+1}}.\qquad \delta\notin\overline{\mathbb{Q}}\ ?
Progress & source assessment
Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
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