On the group of germs of contact transformations (Q2634624)

Summary: 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.