Conformal symplectic geometry of cotangent bundles

We prove a version of the Arnol’d conjecture for Lagrangian submanifolds of conformal symplectic manifolds: a Lagrangian L which has non-zero Morse-Novikov homology for the restriction of the Lee form β cannot be disjoined from itself by a C⁰-small Hamiltonian isotopy. Furthermore for generic such isotopies the number of intersection points equals at least the sum of the free Betti numbers of the Morse-Novikov homology of β. We also give a short exposition of conformal symplectic geometry, aimed at readers who are familiar with (standard) symplectic or contact geometry.