On Contact Integral Calabi Invariant

The problem of calculating of the global invariants for the action of the group of contact diffeomorphisms on itself by conjugations. The integral invariant for this action is obtained. This invariant is the analog of the Calabi invariant for the groups of symplectomorphisms of the unit disk. We nor...

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Bibliographic Details
Published in:Automation and remote control 2020-09, Vol.81 (9), p.1722-1724
Main Authors: Bibikov, P. V., Streltsova, I. S.
Format: Article
Language:English
Subjects:
639/301/1034/1035
639/925/357/995
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Control
Integrals
Invariants
Isomorphism
Large Scale Systems Control
Manifolds
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Robotics
Systems Theory
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Summary:The problem of calculating of the global invariants for the action of the group of contact diffeomorphisms on itself by conjugations. The integral invariant for this action is obtained. This invariant is the analog 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 with respect to this form is our intergal invariant.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117920090118