Abstract
In this article we prove meromorphic continuation of weighted zeta functions Z_f in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016). We obtain a residue formula proving equality between residues of Z_f and invariant Ruelle distributions. We combine this equality with results of Guillarmou et al. (Ann Henri Lebesgue 4:81–119, 2021) in order to relate the residues to Patterson–Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.