Generalized nonlinear superposition principles for polynomial planar vector fields.
Page 1
García, Isaac A., Giacomini, Hector, Giné, Jaume (2005)
Journal of Lie Theory
Campoamor-Stursberg, Rutwig (2004)
Journal of Lie Theory
Marco Antonio Teixeira (1997)
Publicacions Matemàtiques
In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.
Qadir, Asghar (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Alexandr Medvedev (2010)
Archivum Mathematicum
We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application.
Page 1