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    Por favor, use este identificador para citar o enlazar este ítem:https://uvadoc.uva.es/handle/10324/68129

    Título
    Solutions of definable ODEs with regular separation and dichotomy interlacement versus Hardy
    Autor
    Le Gal, Olivier
    Matusinski, Mickaël
    Sanz Sánchez, FernandoAutoridad UVA Orcid
    Año del Documento
    2021
    Editorial
    European Mathematical Society Press
    Descripción
    Producción Científica
    Documento Fuente
    Rev. Mat. Iberoam. 38 (2022), no. 5, 1501–1527
    Résumé
    We introduce a notion of regular separation for solutions of systems of ODEs y'=F(x; y), where F is definable in a polynomially bounded o-minimal structure and y=(y1,y2). Given a pair of solutions with flat contact, we prove that, if one of them has the property of regular separation, the pair is either interlaced or generates a Hardy field. We adapt this result to trajectories of three-dimensional vector fields with definable coefficients. In the particular case of real analytic vector fields, it improves the dichotomy interlaced/separated of certain integral pencils, obtained by F. Cano, R. Moussu and the third author. In this context, we show that the set of trajectories with the regular separation property and asymptotic to a formal invariant curve is never empty and it is represented by a subanalytic set of minimal dimension containing the curve. Finally, we show how to construct examples of formal invariant curves which are transcendental with respect to subanalytic sets, using the so-called (SAT) property, introduced by J.-P. Rolin, R. Shaefke and the third author.
    Palabras Clave
    solutions of ODEs, non-oscillating trajectories of vector fields, o-minimality, Hardy field, transcendental formal solutions
    ISSN
    0213-2230
    Revisión por pares
    SI
    DOI
    10.4171/RMI/1311
    Patrocinador
    F. Sanz Sánchez was partially supported by Ministerio de Ciencia, Spain, process MTM2016-77642-C2-1-P and PID2019-105621GB-I00
    Propietario de los Derechos
    Real Sociedad Matemática Española
    Idioma
    eng
    URI
    https://uvadoc.uva.es/handle/10324/68129
    Tipo de versión
    info:eu-repo/semantics/submittedVersion
    Derechos
    restrictedAccess
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    • DEP96 - Artículos de revista [98]
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    2021_LeG-Mat-San_Rev-Ib-Mat.pdf
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