The Linear Parametrization of Two Dimensional Tori Families in the Restricted Three Body Problem

The Linear Parametrization of Two Dimensional Tori Families in the Restricted Three Body Problem | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Linear Parametrization of Two Dimensional Tori Families in the Restricted Three Body Problem Ian M. Down, Kathleen C. Howell, Manoranjan Majji, Kyle T. Alfriend This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6363486/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Feb, 2026 Read the published version in The Journal of the Astronautical Sciences → Version 1 posted You are reading this latest preprint version Abstract This paper analyzes the relationship between different family branches of 2-dimensional quasi-periodic invariant tori and their linear parametrization in both the circular and elliptical restricted three-body problems. Convergence basins associated with each family branch are defined by the maximal linear parametrization magnitude $\varepsilon$ and computed via flow map reduction under rotational invariance. Convergence basins are correlated with tori stability indices and computational failure modes at the basin edge. Sensitivities of the convergence basin with respect to the dynamical system parameters of non-dimensional mass $\mu$, and eccentricity $e$ are examined. Invariant curve families expose geometric differences in tori family branches. 2-dimensional tori in the vicinity of common $L_1$ and $L_2$ libration point orbit families are analyzed. Regions where particular tori family branches are better represented by the linear parametrization are found, and present an important outcome of this study. invariant tori invariant curve quasi-periodic dynamical systems Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Feb, 2026 Read the published version in The Journal of the Astronautical Sciences → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6363486","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":446048760,"identity":"e1463328-605c-4ddc-9fa1-de7afaa14d5d","order_by":0,"name":"Ian M. 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