Systems Analysis

On contact integral Calabi invariant

P. V. Bibikov^a, I. S. Strel'tsova<sup>b

a</sup> V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
^b Astrakhan State University, Astrakhan

Abstract: The paper is about the problem of the global invariants construction for the action of the group of contact diffeomorphisms on itself by conjugations. The integral invariant is obtained for this action. This invariant is the analogue of the Calabi invariant for the groups of symplectomorphisms of the unit disk. We normalize Cartan form for a given contact diffeomorphism and then consider the volume form on our compact manifold. This volume form is constructed with the help of the normalized Cartan form. The volume of our manifold in relation to this form is our integral invariant.

Keywords: contact diffeomorphism, Calabi invariant, action by conjugations, invariant.

UDC: 514.763.34 + 515.164.13 + 517.95
BBK: 22.15 + 22.161.6

Received: November 21, 2017
Published: March 31, 2018

DOI: 10.25728/ubs.2018.72.2

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