Differential invariants and operators of invariant differentiation of the projectable action of Lie groups

2015 ◽  
Vol 183 (2) ◽  
pp. 619-636 ◽  
Author(s):  
M. M. Goncharovskii ◽  
I. V. Shirokov
Keyword(s):  
Lie Groups ◽  
Differential Invariants ◽  
Invariant Differentiation

scholarly journals Transformation groups on real plane and their differential invariants

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Maryna O. Nesterenko
Keyword(s):  
Lie Algebras ◽  
Differential Invariants ◽  
Transformation Groups ◽  
Real Plane ◽  
Continuous Transformation ◽  
The Real ◽  
Finite Dimensional ◽  
Complete Sets ◽  
Finite Dimensional Lie Algebras ◽  
Invariant Differentiation

Complete sets of bases of differential invariants, operators of invariant differentiation, and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of finite-dimensional Lie algebras on the real plane are revisited.

scholarly journals Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160461 ◽  
Author(s):  
A. A. Gainetdinova ◽  
R. K. Gazizov
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Algebras ◽  
Transformation Group ◽  
Second Order ◽  
Differential Invariants ◽  
Invariant Representation ◽  
Invariant Differentiation

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

Sign in / Sign up

Export Citation Format

Share Document