Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia

[2507.03204] Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Dynamical Systems arXiv:2507.03204 (math) [Submitted on 3 Jul 2025 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia Authors: Yuri Lima , Carlos Matheus , Ian Melbourne View a PDF of the paper titled Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia, by Yuri Lima and 1 other authors View PDF HTML (experimental) Abstract: We consider a class of nonuniformly hyperbolic dynamical systems with a first return time satisfying a central limit theorem (CLT) with nonstandard normalisation $(n\log n)^{1/2}$. For such systems (both maps and flows) we show that it automatically follows that the functional central limit theorem or weak invariance principle (WIP) with normalisation $(n\log n)^{1/2}$ holds for Hölder observables. Our approach streamlines certain arguments in the literature. Applications include various examples from billiards, geodesic flows and intermittent dynamical systems. In this way, we unify existing results as well as obtaining new results. In particular, we deduce the WIP with nonstandard normalisation for Bunimovich stadia as an immediate consequence of the corresponding CLT proved by Bálint & Gouëzel. Comments: Accepted version. To appear in Commun. Math. Phys Subjects: Dynamical Systems (math.DS) Cite as: arXiv:2507.03204 [math.DS] (or arXiv:2507.03204v2 [math.DS] for this version) https://doi.org/10.48550/arXiv.2507.03204 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ian Melbourne [ view email ] [v1] Thu, 3 Jul 2025 22:35:46 UTC (23 KB) [v2] Thu, 9 Apr 2026 21:18:02 UTC (25 KB) Full-text links: Access Paper: View a PDF of the paper titled Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia, by Yuri Lima and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2025-07 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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