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We study vector fields of the plane preserving the form of Liouville. Wepresent their local models up to the natural equivalence relation, and describelocal bifurcations of low codimension. To achieve that, a classification ofunivariate functions is given, according to a relation stricter than contactequivalence. We discuss, in addition, their relation with strictly contactvector fields in dimension three. Analogous results for diffeomorphisms arealso given.

Dynamical systems on the Liouville plane and the related strictly contact systems