Annular Chaos for Non-Wandering Homeomorphisms

[2605.28708] Annular Chaos for Non-Wandering Homeomorphisms Skip to main content Search Submit Donate Log in Mathematics > Dynamical Systems arXiv:2605.28708 (math) [Submitted on 27 May 2026 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: Annular Chaos for Non-Wandering Homeomorphisms Authors: Alejandro Passeggi , Favio Pirán View PDF HTML (experimental) Abstract: We study topological conditions ensuring the presence of rotational chaos for non-wandering or area-preserving annular homeomorphisms. Compared to previous criteria, our main result provides a simpler alternative that avoids the need to locate periodic points, requiring only knowledge of the behavior of certain open sets. This feature is crucial for enabling concrete applications to Poincaré return maps arising in Hamiltonian systems with two degrees of freedom. The resulting topological criterion admits straightforward numerical implementation: a computer can verify all the required conditions using a simple algorithm that relies solely on basic data from the map. We illustrate this approach with the so-called driven pendulum. Subjects: Dynamical Systems (math.DS) Cite as: arXiv:2605.28708 [math.DS] (or arXiv:2605.28708v2 [math.DS] for this version) https://doi.org/10.48550/arXiv.2605.28708 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Favio Pirán [ view email ] [v1] Wed, 27 May 2026 16:33:28 UTC (1,812 KB) [v2] Wed, 26 Aug 2026 18:10:01 UTC (1,726 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2026-05 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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