• Corpus ID: 253553430

Resolvent of vector fields and Lefschetz numbers

  title={Resolvent of vector fields and Lefschetz numbers},
  author={Yann Chaubet and Yannick Guedes Bonthonneau},
. We study the wavefront set of resolvent of arbitrary flows in their region of convergence, to obtain a general formula for their intersection with currents. We provide an application to the topology of surfaces. 

A Ruelle dynamical zeta function for equivariant flows

For proper group actions on smooth manifolds, with compact quotients, we define an equivariant version of the Ruelle dynamical $\zeta$-function for equivariant flows satisfying a nondegeneracy

Poincaré series for surfaces with boundary

We provide a meromorphic continuation for Poincaré series counting orthogeodesics of a negatively curved surface with totally geodesic boundary, as well as for Poincaré series counting geodesic arcs

Dynamical zeta functions for Anosov flows via microlocal analysis

The purpose of this paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for C^\infty Anosov flows. More general results have been recently proved by

Zeta-functions for expanding maps and Anosov flows

Given a real-analytic expanding endomorphism of a compact manifoldM, a meromorphic zeta function is defined on the complex-valued real-analytic functions onM. A zeta function for Anosov flows is

Ruelle zeta function at zero for surfaces

We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known

Smooth Anosov flows: Correlation spectra and stability

By introducing appropriate Banach spaces one can study the spectral properties of the generator of the semigroup defined by an Anosov flow. Consequently, it is possible to easily obtain sharp results

Afterword: Dynamical zeta functions for Axiom A flows

We show that the Ruelle zeta function of any smooth Axiom A flow with orientable stable/unstable spaces has a meromorphic continuation to the entire complex plane. The proof uses the meromorphic

Analytic Torsion, Dynamical Zeta Function, and the Fried Conjecture for Admissible Twists

  • S. Shen
  • Mathematics
    Communications in Mathematical Physics
  • 2021
We show an equality between the analytic torsion and the absolute value at zero of the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an acyclic flat

Poincaré series and linking of Legendrian knots

On a negatively curved surface, we show that the Poincare series counting geodesic arcs orthogonal to some pair of closed geodesic curves has a meromorphic continuation to the whole complex plane.

Control of eigenfunctions on surfaces of variable curvature

We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov geodesic flows. This

Dynamical torsion for contact Anosov flows

We introduce a new object, the dynamical torsion, which extends the potentially ill-defined value at $0$ of the Ruelle zeta function of a contact Anosov flow twisted by an acyclic representation of