This article is cited in 1 paper

Dynamical Systems on the Liouville Plane and the Related Strictly Contact Systems

Stavros Anastassiou

Center of Research and Applications of Nonlinear Systems (CRANS) University of Patras, Department of Mathematics, GR-26500 Rion, Greece

Abstract: We study vector fields of the plane preserving the Liouville form. 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. In addition, we discuss their relation with strictly contact vector fields in dimension three. Analogous results for diffeomorphisms are also given.

Keywords: systems preserving the Liouville form, strictly contact systems, classification, bifurcations.

MSC: 37C15, 37J10, 58K45, 53D10

Received: 14.08.2016
Accepted: 22.11.2016

Language: English

DOI: 10.1134/S1560354716070091

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