Artículos de revistas
Formal Equivalence Between Normal Forms Of Reversible And Hamiltonian Dynamical Systems
Registro en:
Communications On Pure And Applied Analysis. , v. 13, n. 2, p. 703 - 713, 2014.
15340392
10.3934/cpaa.2014.13.703
2-s2.0-84888174336
Autor
Martins R.M.
Institución
Resumen
We show the existence of formal equivalences between 2n-dimensional reversible and Hamiltonian vector fields. The main tool we employ is the normal form theory. 13 2 703 713 Abraham, R., Marsden, J., (1978) Foundations of Mechanics, , Benjamin Cummings, London Antoneli, F., Baptistelli, P.H., Dias, A.P., Manoel, M., Invariant theory and reversible-equivariant vector fields (2009) J. Pure Appl. Algebra, 213, pp. 649-663 Arnold, V.I., (2004) Arnold's Problems, , Springer-Verlag, Berlin Arnold, V.I., Geometrical methods in the theory of ordinary differential equations (1998) Fundamental Principles of Mathematical Sciences, 250. , Springer-Verlag Birkhoff, G.D., Dynamical systems with two degrees of freedom (1917) Trans. Amer. Math. Soc., 18, pp. 199-300 Devaney, R.L., Reversible diffeomorphisms and flows (1976) Trans. Amer. Math. Soc., 218, pp. 89-113 Gaeta, G., Normal forms of reversible dynamical systems (1994) International Journal of Theoretical Physics, 33, pp. 1917-1928 Jacquemard, A., Lima, M.F.S., Teixeira, M.A., Degenerate resonances and branching of periodic orbits (2008) Annali di Matematica Pura Ed Applicata, 187, pp. 105-117 Martins, R.M., Teixeira, M.A., On the Similarity of Hamiltonian and reversible vector fields in 4D (2011) Communications on Pure and Applied Analysis, 10, pp. 1257-1266 Martins, R.M., Teixeira, M.A., Reversible-equivariant systems and matricial equations (2011) Anais da Academia Brasileira de Ciências, 83, pp. 1-16 Van Der Meer, J.C., The hamiltonian hopf bifurcation (1982) Lecture Notes in Mathematics, 1160. , Springer Berlin Van Der Meer, J.C., Sanders, J.A., Vanderbauwhede, A., Hamiltonian structure of the reversible nonsemisimple 1:1 Resonance (1994) Dynamics, Bifurcation and Symmetry: New Trends and New Tools, , Kluwer Academic Publishers Price, G.B., On reversible dynamical systems (1935) Trans. Amer. Math. Soc., 37, pp. 51-79 Sevryuk, M.B., The finite-dimensional reversible KAM theory (1935) Phys. D, 112, pp. 132-147 Teixeira, M.A., Singularities of reversible vector fields (1997) Physica D: Nonlinear Phenomena, 100 (1-2), pp. 101-118. , PII S0167278996001832