Mathieu transformation

The Mathieu transformations make up a subgroup of canonical transformations preserving the differential form
The transformation is named after the French mathematician Émile Léonard Mathieu.
Details.
In order to have this invariance, there should exist at least one relation between formula_2 and formula_3 only (without any formula_4 involved).
where formula_6. When formula_7 a Mathieu transformation becomes a Lagrange point transformation. 