[2407.07286] Natural measures and statistical properties of non-statistical maps with multiple neutral fixed points Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Dynamical Systems arXiv:2407.07286 (math) [Submitted on 10 Jul 2024 ( v1 ), last revised 29 Apr 2026 (this version, v2)] Title: Natural measures and statistical properties of non-statistical maps with multiple neutral fixed points Authors: Douglas Coates , Ian Melbourne , Amin Talebi View a PDF of the paper titled Natural measures and statistical properties of non-statistical maps with multiple neutral fixed points, by Douglas Coates and 1 other authors View PDF HTML (experimental) Abstract: In this article we show that a large class of infinite measure preserving dynamical systems that do not admit physical measures nevertheless exhibit strong statistical properties. In particular, we give sufficient conditions for existence of a distinguished natural measure $\nu$ such that the pushforwards of any absolutely continuous probability measure converge to $\nu$. Moreover, we obtain a distributional limit law for empirical measures. We also extend existing results on the characterisation of the set of almost sure limit points for empirical measures. Our results apply to various intermittent maps with multiple neutral fixed points preserving an infinite $\sigma$-finite absolutely continuous measure. Comments: Minor changes. Final version to appear in J London Math Soc Subjects: Dynamical Systems (math.DS) Cite as: arXiv:2407.07286 [math.DS] (or arXiv:2407.07286v2 [math.DS] for this version) https://doi.org/10.48550/arXiv.2407.07286 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Douglas Coates [ view email ] [v1] Wed, 10 Jul 2024 00:34:14 UTC (33 KB) [v2] Wed, 29 Apr 2026 11:57:49 UTC (38 KB) Full-text links: Access Paper: View a PDF of the paper titled Natural measures and statistical properties of non-statistical maps with multiple neutral fixed points, by Douglas Coates and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2024-07 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