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

Abstract

We study vector fields of the plane preserving the form of Liouville. We present their local models up to the natural equivalence relation, and describe local bifurcations of low codimension. To achieve that, a classification of univariate functions is given, according to a relation stricter than contact equivalence. We discuss, in addition, their relation with strictly contact vector fields in dimension three. Analogous results for diffeomorphisms are also given.

15 pages, 2 figures

References in corpus (2)

• Nilpotent normal form for divergence-free vector fields and volume-preserving maps
• Singularities of Functions on the Martinet Plane, Constrained Hamiltonian Systems and Singular Lagrangians