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Portugaliae Mathematica

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Volume 72, Issue 4, 2015, pp. 393–406
DOI: 10.4171/PM/1972

Published online: 2015-10-29

On the group of germs of contact transformations

Ana Rita Martins[1] and Orlando Neto[2]

(1) Universidade de Lisboa, Portugal
(2) Universidade de Lisboa, Portugal

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.

Keywords: Contact geometry, Legendrian varieties

Martins Ana Rita, Neto Orlando: On the group of germs of contact transformations. Port. Math. 72 (2015), 393-406. doi: 10.4171/PM/1972