Artículos de revistas
Reversible-equivariant Systems And Matricial Equations
Registro en:
Anais Da Academia Brasileira De Ciencias. , v. 83, n. 2, p. 375 - 390, 2011.
13765
2-s2.0-79959311068
Autor
Teixeira M.A.
Martins R.M.
Institución
Resumen
This paper uses tools in group theory and symbolic computing to classify the representations of finite groups with order lower than, or equal to 9 that can be derived from the study of local reversible-equivariant vector fields in R4. The results are obtained by solving matricial equations. In particular, we exhibit the involutions used in a local study of reversible-equivariant vector fields. Based on such approach we present, for each element in this class, a simplified Belitskii normal form. 83 2 375 390 Antoneli, F., Invariant theory and reversible-equivariant vector fields (2009) J Pure Appl Algebra, 213, pp. 649-663 Belitskii, G., C∞-normal forms of local vector fields. Symmetry and perturbation theory (2002) Acta Appl Math, 70, pp. 23-41 Birkhoff, G.D., The restricted problem of three bodies (1915) Rend Circ Mat Palermo, 39, pp. 265-334 Bochner, S., Montgomery, D., Locally Compact Groups of Differentiable Transformations (1946) Ann of Math (2)47, pp. 639-653 Bruno, A.D., Local methods in nonlinear differential equations. Part I. The local method of nonlinear analysis of differential equations. Part II. The sets of analyticity of a normalizing transformation (1989), pp. x+348. , Springer Series in Soviet Mathematics, Springer-Verlag, BerlinBuzzi, C.A., Llibre, J., Medrado, J.C.R., Phase portraits of reversible linear differential systems with cubic homogeneous polynomial nonlinearities having a non-degenerate center at the origin (2009) Qual Theory Dyn Syst, 7, pp. 369-403 Devaney, R., Reversible Diffeomorphisms and Flows (1976) Trans Amer Math Soc, 218, pp. 89-113 Jacquemard, A., Teixeira, M.A., Effective algebraic geometry and normal forms of reversible mappings (2002) Rev Mat Complut, 15, pp. 31-55 Knus, M.-A., The book of involutions (1998), American Mathematical Society, Providence, RI, USALamb, J.S.W., Roberts, J.A.G., Time-Reversal Symmetry in Dynamical Systems: A Survey (1996), 112, pp. 1-39. , Time-reversal symmetry in dynamical systems. Coventry, UK. Phys DMartins, R.M., A estrutura Hamiltoniana dos campos reversíveis em 4D (2008), Master Thesis, Universidade Estadual de Campinas, UNICAMP, Campinas, SP, Brasil. (Unpublished)Teixeira, M.A., Singularities of reversible vector fields (1997) Phys D, 100, pp. 101-118