Short desciption
The FWF-funded stand-alone project "Geometric and ergodic properties of flows" ran from February 2019 until October 2022 and included one PhD student Homero Canales, one postdoc Olga Lukina and the PI Henk Bruin. The central object of study are mthematical flow, both coming from physical models (sch a billiard flows, Lorenz flows and Lorentz flows - Lorenz and Lorentz were two different scientist, wrking in meteorology and particle physics respectively), and more theoretical, such as flows on translation surfaces f finite or infinite genus. The ergodic and statistical properties of such flow are inverstigated, describing weak mixing, mixing and mixing rates, and futher statistical properties and limit theorems. One particular flow, which is central to the PhD project of Homero Canales, was a neutral Lorenz flow in which the organising saddle is neutral, giving rise to polynmial mixing rates of the flow.

Publications completed or initiated in this project

• Henk Bruin On volume preserving almost Anosov flows. Preprint 2019 updated 2022 [.pdf] and arXiv version. To appear in Monatsh. Math.
• On Sinai billiards on flat surfaces with horns. Preprint 2020 (revised Jan. 2021) [.pdf] and arXiv version Journ. Stat. Phys. 183 (18) (2021). Doi:10.1007/s10955-021-02746-w
• Henk Bruin, Olga Lukina, Rotated odometers. Preprint 2021, updated in August 2022: (updated, and arXiv version
• Henk Bruin, Olga Lukina, Rotated odometers and actions on rooted trees. Preprint 2021 (updated 2022) [.pdf], and arXiv version. Fund. Math. 260 (2023) 233-249. (electronic DOI: 10.4064/fm74-10-2022)
• Péter Bálint, Henk Bruin and Dalia Terhesiu, Lorentz gas with small scatterers, Preprint 2021 (updated November 2022) [.pdf], and arXiv version, to appear in Prob. Th. and Rel. Fields.
• Henk Bruin and Homero Canales Mixing rates of the geometrical neutral Lorenz model In preparation.

• Henk Bruin, Dalia Terhesiu, Regular variation and rates of mixing for infinite measure preserving almost Anosov diffeomorphisms Preprint 2017 (updated Jan 2018) [.pdf] arXiv version. Ergod. Th. and Dyn. Sys. Ergod. Th. and Dyn. Sys. 40 2020, 663-698, doi.org/10.1017/etds.2018.58).