Resolvent of vector fields and Lefschetz numbers
@inproceedings{Chaubet2022ResolventOV, title={Resolvent of vector fields and Lefschetz numbers}, author={Yann Chaubet and Yannick Guedes Bonthonneau}, year={2022} }
. 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.
One Citation
A Ruelle dynamical zeta function for equivariant flows
- Mathematics
- 2023
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…
22 References
Poincaré series for surfaces with boundary
- MathematicsNonlinearity
- 2022
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
- Mathematics
- 2013
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
- Mathematics
- 1976
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
- Mathematics
- 2016
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
- Mathematics
- 2007
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
- Mathematics
- 2018
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
- MathematicsCommunications 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
- Mathematics
- 2020
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
- MathematicsJournal of the American Mathematical Society
- 2021
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
- Mathematics
- 2019
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…