VECTOR FIELDS, VARIATIONAL EQUATIONS AND COMMUTATORS
2012 ◽
Vol 22
(08)
◽
pp. 1250190
Keyword(s):
We study autonomous systems of first order ordinary differential equations, their corresponding vector fields and the autonomous system corresponding to the vector field of the commutator of two such autonomous systems. These vector fields form a Lie algebra. From the variational equations of these autonomous systems, we form new vector fields consisting of the sum of the two vector fields. We show that these new vector fields also form a Lie algebra. Results about fixed points, first integrals and the divergence of the vector fields are also presented.
2007 ◽
Vol 04
(07)
◽
pp. 1217-1230
2010 ◽
Vol 2010
◽
pp. 1-13
◽
2020 ◽
pp. 87-96
Keyword(s):
2008 ◽
Vol 05
(07)
◽
pp. 1057-1063
1991 ◽
Vol 11
(3)
◽
pp. 443-454
◽