TY  - JOUR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Differential invariants of a class of Lagrangian systems with two degrees of freedom
JF  - Journal of mathematical analysis and applications
KW  - Equivalence
KW  - Differential invariant
KW  - Euler-Lagrange equations
Y1  - 2014
U6  - https://doi.org/10.1016/j.jmaa.2013.08.015
SN  - 0022-247X
SN  - 1096-0813
VL  - 410
IS  - 2
SP  - 733
EP  - 749
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Solution of the equivalence problem for the third Painleve equation
JF  - Journal of mathematical physics
N2  - We find necessary conditions for a second order ordinary differential equation to be equivalent to the Painleve III equation under a general point transformation. Their sufficiency is established by reduction to known results for the equations of the form y ' = f (x, y). We consider separately the generic case and the case of reducibility to an autonomous equation. The results are illustrated by the primary resonance equation.
Y1  - 2015
U6  - https://doi.org/10.1063/1.4905383
SN  - 0022-2488
SN  - 1089-7658
VL  - 56
IS  - 1
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - INPR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Differential invariants of a class of Lagrangian systems with two degrees of freedom
N2  - We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 2 
KW  - equivalence
KW  - invariant
KW  - Euler-Lagrange equations
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63129
ER  -