| Автор | Giambò, R. |
| Автор | Javaloyes, M. Á. |
| Дата выпуска | 2007 |
| dc.description | We give the notion of a conjugate instant along a solution of the relativistic Lorentz force equation (LFE). Electromagnetic conjugate instants are defined as zeros of solutions of the linearized LFE with fixed value of the charge-to-mass ratio; equivalently, we show that electromagnetic conjugate points are the critical values of the corresponding electromagnetic exponential map. We prove a second-order variational principle relating every solution of the LFE to a canonical lightlike geodesic in a Kaluza–Klein manifold, whose metric is defined using the value of the charge-to-mass ratio. Electromagnetic conjugate instants correspond to conjugate points along the lightlike geodesic, and therefore they are isolated; based on such correspondence and on a recent result of bifurcation for light rays, we prove a bifurcation result for solutions of the LFE in the exact case. |
| Издатель | Cambridge University Press |
| Название | A second-order variational principle for the Lorentz force equation: conjugacy and bifurcation |
| DOI | 10.1017/S0308210506000497 |
| Electronic ISSN | 1473-7124 |
| Print ISSN | 0308-2105 |
| Журнал | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |
| Том | 137 |
| Первая страница | 923 |
| Последняя страница | 936 |
| Аффилиация | Giambò R.; Università di Camerino |
| Аффилиация | Javaloyes M. Á.; Politecnico di Bari |
| Выпуск | 5 |
