On a homoclinic splitting problem (Q5938498)

The authors develop an idea by Sauzin to measure a splitting of separatrices by a ``splitting distance function.'' It is based on a representation of the stable and unstable manifolds of a hyperbolic torus as exact Lagrangian submanifolds of a phase space. The splitting distance function is the difference of the generating functions of these submanifolds. The authors justify these arguments supplying rigorous arguments for existence of such a function by using a special version of the KAM theorem previously proven by them.