INFINITESIMAL DERIVATIVE OF THE BOTT CLASSAND THE SCHWARZIAN DERIVATIVES

摘要

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