Iteration of closed geodesics in stationary Lorentzian manifolds
| dc.creator | Javaloyes, Miguel Angel | |
| dc.creator | de Lima, Levi Lopes | |
| dc.creator | Piccione, Paolo | |
| dc.date | 2007-05-04 | |
| dc.date | 2007-06-12 | |
| dc.date.accessioned | 2026-07-07T08:05:04Z | |
| dc.date.available | 2026-07-07T08:05:04Z | |
| dc.description | Following the lines of a celebrated result by R. Bott (Comm. Pure Appl. Math. 9, 1956) we study the Morse index of the iterated of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic $γ$, we prove the existence of a locally constant integer valued map $Λ_γ$ on the unit circle with the property that the Morse index of the iterated $γ^N$ is equal, up to a correction term $ε_γ\in\{0,1\}$, to the sum of the values of $Λ_γ$ at the $N$-th roots of unity. The discontinuities of $Λ_γ$ occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincaré map of $γ$. We discuss some applications of the theory. | |
| dc.description | LaTeX2e, amsart, 22 pages. Acknowledgements of financial support added | |
| dc.identifier | https://arxiv.org/abs/0705.0589 | |
| dc.identifier | http://arxiv.org/abs/0705.0589 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130160 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C22; 58E10; 53C50; 37B30 | |
| dc.title | Iteration of closed geodesics in stationary Lorentzian manifolds | |
| dc.type | text |