[2203.12156] Accessible hyperbolic components in anti-holomorphic dynamics Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Dynamical Systems arXiv:2203.12156 (math) [Submitted on 23 Mar 2022 ( v1 ), last revised 1 May 2026 (this version, v3)] Title: Accessible hyperbolic components in anti-holomorphic dynamics Authors: Hiroyuki Inou , Tomoki Kawahira View a PDF of the paper titled Accessible hyperbolic components in anti-holomorphic dynamics, by Hiroyuki Inou and 1 other authors View PDF HTML (experimental) Abstract: The tricorn, the connectedness locus of the anti-holomorphic quadratic family, is known to be non-locally connected. The boundary of every hyperbolic component of odd period contains arcs that are inaccessible from the complement of the tricorn. As the period increases, the decorations become more and more complicated, and it seems natural to think that every hyperbolic component of sufficiently large and odd period is inaccessible. Contrary to this expectation, we show that the tricorn contains infinitely many hyperbolic components that are accessible from the complement. Comments: 28 pages, 7 figures Subjects: Dynamical Systems (math.DS) MSC classes: 37F10 Cite as: arXiv:2203.12156 [math.DS] (or arXiv:2203.12156v3 [math.DS] for this version) https://doi.org/10.48550/arXiv.2203.12156 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hiroyuki Inou [ view email ] [v1] Wed, 23 Mar 2022 03:05:44 UTC (6,736 KB) [v2] Thu, 3 Jul 2025 15:02:48 UTC (6,738 KB) [v3] Fri, 1 May 2026 06:54:14 UTC (6,860 KB) Full-text links: Access Paper: View a PDF of the paper titled Accessible hyperbolic components in anti-holomorphic dynamics, by Hiroyuki Inou and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2022-03 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