Generating families on arboreal graphs

The paper is devoted to the study of exact curves on Arborealized Liouville surfaces. We introduce the notion of a generating family for such curves. Our main statement is a hamiltonian lifting property: the set of curves admitting a generating family is closed with respect to Hamiltonian isotopes. This is part of the author’s future thesis. It will be translated into English within a few weeks. In the future, we plan to generalize our results in several directions and find applications.