An algorithm to detect and rigorously verify blenders

[2603.21603] An algorithm to detect and rigorously verify blenders Skip to main content Search Submit Donate Log in Mathematics > Dynamical Systems arXiv:2603.21603 (math) [Submitted on 23 Mar 2026 ( v1 ), last revised 25 Aug 2026 (this version, v3)] Title: An algorithm to detect and rigorously verify blenders Authors: Andy Hammerlindl , Natalia McAlister , Warwick Tucker View PDF HTML (experimental) Abstract: We present a characterisation of blenders based on mapping properties of certain sets of curves that can be rigorously verified by computer-assisted methods. We develop an algorithm to construct these sets of curves that requires only a rough approximation of the strong unstable direction in a prescribed region. Since our approach does not rely on precise data, such as the exact location of invariant manifolds or fixed points, it provides a systematic framework to verify blenders in explicit examples. Here, we apply this framework to rigorously verify that a family of three-dimensional Hénon-like maps presents blenders. Comments: 21 pages, 8 figures Subjects: Dynamical Systems (math.DS) MSC classes: 37D30, 37M21, 65G20 Cite as: arXiv:2603.21603 [math.DS] (or arXiv:2603.21603v3 [math.DS] for this version) https://doi.org/10.48550/arXiv.2603.21603 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Natalia McAlister [ view email ] [v1] Mon, 23 Mar 2026 05:55:40 UTC (271 KB) [v2] Thu, 26 Mar 2026 22:27:56 UTC (272 KB) [v3] Tue, 25 Aug 2026 04:31:29 UTC (407 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Ancillary-file links: Ancillary files ( details ) : README.txt buildsettings.cc cheb.h common.h construct.cc diagnose.py json.hpp jsonify.h makefile plot.py run_all.sh verify.cc (7 additional files not shown) Current browse context: math.DS < prev | next > new | recent | 2026-03 Change to browse by: math References & Citations NASA ADS 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) Major funding support from

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