Dan Asimov wrote:
In the complex plane C, consider the differential equation
dz/dt = i(z^3-z) ... F(z,t) : = the solution z(t) of [dz/dt = i(z^3-z)] for which z(0) = z. ... (*) for all z in U, we have F(z,pi) = z ... (**) for all z in V, we have F(z,pi) ≠ z ... But wait, there's more. The Identity Theorem (sometimes known as the Permanence Theorem) in complex variables implies that if two analytic functions (like F(z,pi) and z) are equal on a nonempty open set in C, then they are equal everywhere.
... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... Why should we assume F(--,pi) is analytic? -- g