Isaac Scientific Publishing

Advances in Analysis

Report on the Absolute Differential Equations I

Download PDF (690.1 KB) PP. 41 - 61 Pub. Date: January 15, 2017

DOI: 10.22606/aan.2017.11007

Author(s)

  • Veronika Chrastinová*
    Brno University of Technology, Faculty of Civil Engineering, Department of Mathematics, Veverí 331/95, 602 00 Brno, Czech Republic
  • Václav Tryhuk
    Brno University of Technology, Faculty of Civil Engineering, AdMaS centre, Purkynova 139, 612 00 Brno, Czech Republic

Abstract

The article provides a survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract mathematical theory in the Bourbaki sense with its own concepts and technical tools follows. In particular the external, internal, generalized and higher–order symmetries and infinitesimal symmetries together with the E. Cartan’s prolongations, various characteristics, the involutivity and the controllability structures are clarified in genuinely coordinate–free terms without any use of the common jet mechanisms.

Keywords

Higher–order transformations, symmetry, diffiety, involutivity, controllability, characteristics.

References

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