Tangential homoclinic points for Lozi maps

[2412.12536] Tangential homoclinic points for Lozi maps Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Dynamical Systems arXiv:2412.12536 (math) [Submitted on 17 Dec 2024 ( v1 ), last revised 28 Mar 2026 (this version, v2)] Title: Tangential homoclinic points for Lozi maps Authors: Kristijan Kilassa Kvaternik View a PDF of the paper titled Tangential homoclinic points for Lozi maps, by Kristijan Kilassa Kvaternik View PDF HTML (experimental) Abstract: For the family of Lozi maps, we study homoclinic points for the saddle fixed point $X$ in the first quadrant. Specifically, in the parameter space, we examine the boundary of the region in which homoclinic points for $X$ exist. For all parameters on that boundary, all intersections of the stable and unstable manifold of $X$, apart from $X$, are tangential, or these manifolds intersect along a segment. We ultimately prove that for such parameters, all possible homoclinic points for $X$ are iterates of two special points $Z$ and $V$, or iterates of points on a segment joining $V$ with an iterate of $Z$. Additionally, we describe the parameter curves that form the boundary and provide explicit equations for several of them. Comments: 34 pages, 12 figures. Implemented changes based on the referee reports, including the case of homoclinic intersections along a segment. Accepted for publication in Journal of Dynamics and Differential Equations Subjects: Dynamical Systems (math.DS) MSC classes: 37E30 (Primary) 37D05 (Secondary) Cite as: arXiv:2412.12536 [math.DS] (or arXiv:2412.12536v2 [math.DS] for this version) https://doi.org/10.48550/arXiv.2412.12536 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Dynamics and Differential Equations (2026) Related DOI : https://doi.org/10.1007/s10884-026-10505-2 Focus to learn more DOI(s) linking to related resources Submission history From: Kristijan Kilassa Kvaternik [ view email ] [v1] Tue, 17 Dec 2024 05:00:13 UTC (1,220 KB) [v2] Sat, 28 Mar 2026 01:09:25 UTC (1,701 KB) Full-text links: Access Paper: View a PDF of the paper titled Tangential homoclinic points for Lozi maps, by Kristijan Kilassa Kvaternik View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2024-12 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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