Laplace transform, dynamics and spectral geometry
| dc.creator | Burghelea, Dan | |
| dc.creator | Haller, Stefan | |
| dc.date | 2004-05-03 | |
| dc.date | 2005-01-17 | |
| dc.date.accessioned | 2026-07-07T05:07:54Z | |
| dc.date.available | 2026-07-07T05:07:54Z | |
| dc.description | We consider vector fields $X$ on a closed manifold $M$ with rest points of Morse type. For such vector fields we define the property of exponential growth. A cohomology class $ξ\in H^1(M;\mathbb R)$ which is Lyapunov for $X$ defines counting functions for isolated instantons and closed trajectories. If $X$ has exponential growth property we show, under a mild hypothesis generically satisfied, how these counting functions can be recovered from the spectral geometry associated to $(M,g,ω)$ where $g$ is a Riemannian metric and $ω$ is a closed one form representing $ξ$. This is done with the help of Dirichlet series and their Laplace transform. | |
| dc.description | added a reference and dropped an appendix | |
| dc.identifier | https://arxiv.org/abs/math/0405037 | |
| dc.identifier | http://arxiv.org/abs/math/0405037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71045 | |
| dc.subject | Differential Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | 57R20; 57R58; 57R70; 57Q10; 58J52 | |
| dc.title | Laplace transform, dynamics and spectral geometry | |
| dc.type | text |