• Corpus ID: 245650778

Dynamical zeta functions for billiards

@inproceedings{Chaubet2022DynamicalZF,
  title={Dynamical zeta functions for billiards},
  author={Yann Chaubet and V. Petkov},
  year={2022}
}
. Let D ⊂ R d , d (cid:62) 2 , be the union of a finite collection of pairwise disjoint strictly convex compact obstacles. Let µ j ∈ C , Im µ j > 0 be the resonances of the Laplacian in the exterior of D with Neumann or Dirichlet boundary condition on ∂D . For d odd, u ( t ) = (cid:80) j e i | t | µ j is a distribution in D (cid:48) ( R \ { 0 } ) and the Laplace transforms of the leading singularities of u ( t ) yield the dynamical zeta functions η N , η D for Neumann and Dirichlet boundary… 
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References

SHOWING 1-10 OF 51 REFERENCES

Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems

In this article we prove meromorphic continuation of weighted zeta functions Zf in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and

Resonances and weighted zeta functions for obstacle scattering via smooth models

. We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular

Mathematical Theory of Scattering Resonances

FBI Transform in Gevrey Classes and Anosov Flows

An analytic FBI transform is built on compact manifolds without boundary, that satisfies all the expected properties. It enables the study of microlocal analytic regularity on such manifolds. This

Geometry of multi-dimensional dispersing billiards

— Geometric properties of multi-dimensional dispersing billiards are studied in this paper. On the one hand, non-smooth behaviour in the singularity subman­ ifolds of the system is discovered (this

Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps: A Functional Approach

Transfer operators associated with a dynamical system T and a weight g are important tools to understand the statistical properties of T , under appropriate smoothness and hyperbolicity conditions.

Geometry of the Generalized Geodesic Flow and Inverse Spectral Problems

This book is a new edition of a title originally published in1992. No other book has been published that treats inverse spectral and inverse scattering results by using the so called Poisson

Meromorphic zeta functions for analytic flows

We extend to hyperbolic flows in all dimensions Rugh's results on the meromorphic continuation of dynamical zeta functions. In particular we show that the Ruelle zeta function of a negatively curved
...