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Laplace transform, dynamics and spectral geometry | | Dan Burghelea
; Stefan Haller
; | | Date: |
3 May 2004 | | Subject: | Differential Geometry; Dynamical Systems MSC-class: 57R20; 57R58; 57R70; 57Q10; 58J52 | math.DG math.DS | | Abstract: | 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 $xiin H^1(M;mathbb R)$ 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 $(M,g,omega)$ where $g$ is a Riemannian metric and $omega$ is a closed one form representing $xi$. This is done with the help of Dirichlet series and their Laplace transform. | | Source: | arXiv, math.DG/0405037 | | Services: | Forum | Review | PDF | Favorites | |
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