Displaying similar documents to “Hyperbolic systems on nilpotent covers”

The return sequence of the Bowen-Series map for punctured surfaces

Manuel Stadlbauer (2004)

Fundamenta Mathematicae

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For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the...

On the spectral theory and dynamics of asymptotically hyperbolic manifolds

Julie Rowlett (2010)

Annales de l’institut Fourier

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We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.