# 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…

## 2 Citations

### Semiclassical formulae for Wigner distributions

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In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics.…

### Resonances and weighted zeta functions for obstacle scattering via smooth models

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. 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…

## References

SHOWING 1-10 OF 51 REFERENCES

### Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems

- Mathematics
- 2021

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

- Mathematics
- 2021

. 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…

### FBI Transform in Gevrey Classes and Anosov Flows

- Mathematics
- 2020

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

- Mathematics
- 2005

— 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

- Mathematics
- 2018

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.…

### The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis

- Mathematics
- 1983

### Geometry of the Generalized Geodesic Flow and Inverse Spectral Problems

- Mathematics
- 2017

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

- Mathematics
- 1995

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…