On a conjecture of De Giorgi related to homogenization
On a conjecture of De Giorgi related to homogenization
For a periodic vector field F, let $$X^\varepsilon $$ solve the dynamical system $$\begin{aligned} \frac{{\hbox {d}}{\hbox {X}}^{\varepsilon }}{{\hbox {d}}t} = {{F}}\left( \frac{{X}^{\varepsilon }}{\varepsilon }\right) . \end{aligned}$$ In (Set Valued Anal 2(1–2):175–182, 1994) Ennio De Giorgi enquiers whether from the existence of the limit $$ X^0(t):=\lim \nolimits _{\varepsilon \rightarrow 0} X^\varepsilon …