A Green Function Approach to Smooth Nonautonomous Topological Equivalence with Unbounded Nonlinearities under $(μ,ν)$--Dichotomies

[2608.14715] A Green Function Approach to Smooth Nonautonomous Topological Equivalence with Unbounded Nonlinearities under $(μ,ν)$--Dichotomies Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Dynamical Systems arXiv:2608.14715 (math) [Submitted on 11 Aug 2026] Title: A Green Function Approach to Smooth Nonautonomous Topological Equivalence with Unbounded Nonlinearities under $(μ,ν)$--Dichotomies Authors: Fernanda Torres View a PDF of the paper titled A Green Function Approach to Smooth Nonautonomous Topological Equivalence with Unbounded Nonlinearities under $(\mu,\nu)$--Dichotomies, by Fernanda Torres View PDF HTML (experimental) Abstract: We study the smooth topological equivalence between a nonautonomous linear system on the positive half-line and a quasilinear perturbation whose nonlinear part is not assumed to be globally bounded with respect to the state variable. The linear equation is assumed to admit a $(\mu,\nu)$--dichotomy, and the construction is carried out through the Green operator associated with this dichotomy. The usual global boundedness of the perturbation is replaced by locally uniform Green-integrability conditions along the relevant linear and nonlinear solutions. Under a smallness condition involving the global Lipschitz constant of the perturbation and the Green operator, we first construct Palmer-type maps which give a continuous topological equivalence on $\mathbb R^+$. We then impose Green-integrability conditions on the successive variational equations and a further first-order smallness condition which guarantees the invertibility of the derivative of the inverse map. Under these assumptions, the equivalence is of class $C^r$. We also provide a class of examples for which the perturbation is unbounded with respect to the space variable and all the hypotheses can be verified directly. Subjects: Dynamical Systems (math.DS) ; Classical Analysis and ODEs (math.CA) MSC classes: 37C60, 37B25 Cite as: arXiv:2608.14715 [math.DS] (or arXiv:2608.14715v1 [math.DS] for this version) https://doi.org/10.48550/arXiv.2608.14715 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Fernanda Torres [ view email ] [v1] Tue, 11 Aug 2026 20:56:11 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled A Green Function Approach to Smooth Nonautonomous Topological Equivalence with Unbounded Nonlinearities under $(\mu,\nu)$--Dichotomies, by Fernanda Torres View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2026-08 Change to browse by: math math.CA 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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