Laplace transform, dynamics and spectral geometry

dc.creatorBurghelea, Dan
dc.creatorHaller, Stefan
dc.date2004-05-03
dc.date2005-01-17
dc.date.accessioned2026-07-07T05:07:54Z
dc.date.available2026-07-07T05:07:54Z
dc.descriptionWe 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.descriptionadded a reference and dropped an appendix
dc.identifierhttps://arxiv.org/abs/math/0405037
dc.identifierhttp://arxiv.org/abs/math/0405037
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71045
dc.subjectDifferential Geometry
dc.subjectDynamical Systems
dc.subject57R20; 57R58; 57R70; 57Q10; 58J52
dc.titleLaplace transform, dynamics and spectral geometry
dc.typetext

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