{"_id":"58872","abstract":[{"lang":"eng","text":"Given a non-compact semisimple real Lie group $G$ and an Anosov subgroup\r\n$\\Gamma$, we utilize the correspondence between $\\mathbb R$-valued additive\r\ncharacters on Levi subgroups $L$ of $G$ and $\\mathbb R$-affine homogeneous line\r\nbundles over $G/L$ to systematically construct families of non-empty domains of\r\nproper discontinuity for the $\\Gamma$-action. If $\\Gamma$ is torsion-free, the\r\nanalytic dynamical systems on the quotients are Axiom A, and assemble into a\r\nsingle partially hyperbolic multiflow. Each Axiom A system admits global\r\nanalytic stable/unstable foliations with non-wandering set a single basic set\r\non which the flow is conjugate to Sambarino's refraction flow, establishing\r\nthat all refraction flows arise in this fashion. Furthermore, the $\\mathbb\r\nR$-valued additive character is regular if and only if the associated Axiom A\r\nsystem admits a compatible pseudo-Riemannian metric and contact structure,\r\nwhich we relate to the Poisson structure on the dual of the Lie algebra of $G$."}],"title":"Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups","type":"preprint","user_id":"70575","citation":{"apa":"Delarue, B., Monclair, D., &#38; Sanders, A. (2025). Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups. In <i>arXiv:2502.20195</i>.","ama":"Delarue B, Monclair D, Sanders A. Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups. <i>arXiv:250220195</i>. Published online 2025.","short":"B. Delarue, D. Monclair, A. Sanders, ArXiv:2502.20195 (2025).","mla":"Delarue, Benjamin, et al. “Locally Homogeneous Axiom A Flows II: Geometric Structures for Anosov  Subgroups.” <i>ArXiv:2502.20195</i>, 2025.","ieee":"B. Delarue, D. Monclair, and A. Sanders, “Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups,” <i>arXiv:2502.20195</i>. 2025.","bibtex":"@article{Delarue_Monclair_Sanders_2025, title={Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups}, journal={arXiv:2502.20195}, author={Delarue, Benjamin and Monclair, Daniel and Sanders, Andrew}, year={2025} }","chicago":"Delarue, Benjamin, Daniel Monclair, and Andrew Sanders. “Locally Homogeneous Axiom A Flows II: Geometric Structures for Anosov  Subgroups.” <i>ArXiv:2502.20195</i>, 2025."},"year":"2025","publication":"arXiv:2502.20195","external_id":{"arxiv":["2502.20195"]},"status":"public","date_updated":"2025-02-28T10:33:03Z","author":[{"first_name":"Benjamin","last_name":"Delarue","full_name":"Delarue, Benjamin","id":"70575"},{"full_name":"Monclair, Daniel","last_name":"Monclair","first_name":"Daniel"},{"last_name":"Sanders","first_name":"Andrew","full_name":"Sanders, Andrew"}],"language":[{"iso":"eng"}],"date_created":"2025-02-28T10:31:36Z"}