On the group of germs of contact transformations

Abstract

We show that the germ of a contact transformation $\Phi$ can be written in a unique way as a product ${\Phi }_1{\Phi }_2$, where ${\Phi }_1$ only depends on the derivative of $\Phi$ and the derivative of ${\Phi }_2$ is trivial. We show that each contact transformation with trivial derivative can be constructed solving a convenient Cauchy problem.