Aubry-Mather theory and the inverse spectral problem for planar convex domains (Q1961348)

Suppose \(\Omega\subset \mathbb{R}^2\) is a strictly convex domain with smooth boundary \(\partial\Omega\). The marked length spectrum \({\mathfrak {ML}}(\Omega)\) is the function that associates to each rational number \(m/n\) the maximal length of closed geodesics in \(\Omega\) having rotation number \(m/n\). The main goal of this paper is to establish a link between the inverse spectral problem for \({\mathfrak {ML}}(\Omega)\) and what is known as Aubry-Mather theory in dynamical systems, that investigates action-minimizing orbits of monotone twist mappings.