{"status":"public","_id":"53414","external_id":{"arxiv":["2403.14257"]},"date_created":"2024-04-11T12:31:34Z","user_id":"70575","year":"2024","author":[{"last_name":"Delarue","full_name":"Delarue, Benjamin","first_name":"Benjamin","id":"70575"},{"first_name":"Daniel","full_name":"Monclair, Daniel","last_name":"Monclair"},{"full_name":"Sanders, Andrew","last_name":"Sanders","first_name":"Andrew"}],"citation":{"ama":"Delarue B, Monclair D, Sanders A. Locally homogeneous Axiom A flows I: projective Anosov subgroups and  exponential mixing. <i>arXiv:240314257</i>. Published online 2024.","bibtex":"@article{Delarue_Monclair_Sanders_2024, title={Locally homogeneous Axiom A flows I: projective Anosov subgroups and  exponential mixing}, journal={arXiv:2403.14257}, author={Delarue, Benjamin and Monclair, Daniel and Sanders, Andrew}, year={2024} }","ieee":"B. Delarue, D. Monclair, and A. Sanders, “Locally homogeneous Axiom A flows I: projective Anosov subgroups and  exponential mixing,” <i>arXiv:2403.14257</i>. 2024.","short":"B. Delarue, D. Monclair, A. Sanders, ArXiv:2403.14257 (2024).","apa":"Delarue, B., Monclair, D., &#38; Sanders, A. (2024). Locally homogeneous Axiom A flows I: projective Anosov subgroups and  exponential mixing. In <i>arXiv:2403.14257</i>.","mla":"Delarue, Benjamin, et al. “Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and  Exponential Mixing.” <i>ArXiv:2403.14257</i>, 2024.","chicago":"Delarue, Benjamin, Daniel Monclair, and Andrew Sanders. “Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and  Exponential Mixing.” <i>ArXiv:2403.14257</i>, 2024."},"type":"preprint","department":[{"_id":"548"}],"language":[{"iso":"eng"}],"date_updated":"2024-04-11T12:39:02Z","title":"Locally homogeneous Axiom A flows I: projective Anosov subgroups and  exponential mixing","abstract":[{"text":"By constructing a non-empty domain of discontinuity in a suitable homogeneous\r\nspace, we prove that every torsion-free projective Anosov subgroup is the\r\nmonodromy group of a locally homogeneous contact Axiom A dynamical system with\r\na unique basic hyperbolic set on which the flow is conjugate to the refraction\r\nflow of Sambarino. Under the assumption of irreducibility, we utilize the work\r\nof Stoyanov to establish spectral estimates for the associated complex Ruelle\r\ntransfer operators, and by way of corollary: exponential mixing, exponentially\r\ndecaying error term in the prime orbit theorem, and a spectral gap for the\r\nRuelle zeta function. With no irreducibility assumption, results of\r\nDyatlov-Guillarmou imply the global meromorphic continuation of zeta functions\r\nwith smooth weights, as well as the existence of a discrete spectrum of\r\nRuelle-Pollicott resonances and (co)-resonant states. We apply our results to\r\nspace-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds\r\nof Danciger-Gu\\'eritaud-Kassel, and the Benoist-Hilbert geodesic flow for\r\nstrictly convex real projective manifolds.","lang":"eng"}],"publication":"arXiv:2403.14257"}