3 problems

Let $F$ be a twist map, let $c_1<c_2$, and let $\Lambda_{[c_1,c_2]}$ be the set of orbits corresponding to minimal configurations with $c\in[c_1,c_2]$. Let $\alpha$ denote the rele…

Let $M$ be a manifold and let $L$ be a Tonelli Lagrangian on $TM$. For a cohomology class $c\in H^1(M,\mathbb{R})$, let the Aubry set of $(L+f,c)$ denote the Aubry set associated w…

Mañé's Aubry-set conjecture. The set $\mathcal{O}_3(L)$ is residual in $C^{\infty}(M)$. The source states that this conjecture is equivalent to the strong conjecture on generic min…