Infinitesimal derivative of the Bott class and the Schwarzian derivatives

Abstract

An infinitesimal derivative of the Bott class is defined by generalizing Heitsch'es construction. We prove a formula relating the infinitesimal derivative to the Schwarzian derivatives, which gives a generalization of the Maszczyk formula for the Godbillon-Vey class of real codimension-one foliations. As an application, a residue of infinitesimal derivatives with respect to the Julia set in the sense of Ghys, Gomez-Mont and Saludes is introduced.