5 problems

Let $f(t)$ be the quasi-periodic function in the preceding perturbative construction, let $M(f)$ denote its mean, and let $g$ be defined by the expansion … with…

Asymptotic-convergence conjecture. The differences between the various calculation methods are due to the asymptotic nature of the calculations, whose radius of convergence is smal…

Purely imaginary parameter conjecture. No solutions of the fixed-point equation exist when $\varepsilon$ is purely imaginary, because the zero divisors can be regarded as resonance…

Optimal-domain conjecture. The optimal domain of $\varepsilon$ on which $U_{\varepsilon}$ can be considered as a function does not extend to the imaginary axis.

Optimality conjecture. This domain is optimal: for these small parameter values and general forcing and nonlinearity, regular solutions do not exist.