C 1 non-integrability of a hydrogen atom in a circularly polarized microwave field
Tóm tắt
Barrabés et al. [Physica D, 241(4), 333–349, 2012] consider the problem of the hydrogen atom interacting with a circularly polarized microwave field modeled as a planar perturbed Kepler problem. For different values of the parameter, the authors offer some numerical evidence of the non-integrability of this problem. The objective of the present work is to give an analytical proof of the C1 non-integrability of this problem for any value of the parameter using the averaging theory as a main tool.
Tài liệu tham khảo
E. Barrabés, M. Ollé, F. Borondo, D. Farrelly, J. Mondelo, Physica D 241, 333 (2012)
R. Abraham, J. E. Marsden, Foundations of Mechanics, (Benjamin, Reading, Masachusets, 1978)
V. I. Arnold, V. Kozlov, A. Neishtadt, Dynamical Systems III. Mathematical Aspects of Classical and Celestial Mechanics, Third Edition, Encyclopaedia of Mathematical Science, (Springer, Berlin, 2006)
A. Deprit, Celest. Mech. Dyn. Ast. 51, 201 (1991)
H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Vol. I, (Gauthier-Villars, Paris 1899)
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, (Universitext, Springer, 1991)
E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Mathematical Library, (Cambridge University Press, 1989)