Dynamics, Laplace transform and spectral geometry
نویسندگان
چکیده
منابع مشابه
Laplace Transform, Dynamics and Spectral Geometry
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 ∈ H(M ;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, that these counting f...
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We consider a vector field X on a closed manifold which admits a Lyapunov one form. We assume X has Morse type zeros, satisfies the Morse– Smale transversality condition and has non-degenerate closed trajectories only. For a closed one form η, considered as flat connection on the trivial line bundle, the differential of the Morse complex formally associated to X and η is given by infinite serie...
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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 ∈ H(M ;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 fu...
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متن کاملDynamics, Spectral Geometry and Topology
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are the rest points, instantons and closed trajectories. One discusses their counting in the case of a generic vector field which has some additional properties s...
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ژورنال
عنوان ژورنال: Journal of Topology
سال: 2007
ISSN: 1753-8416
DOI: 10.1112/jtopol/jtm005