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oai:uvadoc.uva.es:10324/681292024-12-03T14:36:52Zcom_10324_1129com_10324_931com_10324_894col_10324_1193

Le Gal, Olivier e1c1e112-ed9a-43b4-bd10-702836a02db6 500 Matusinski, Mickaël 8cd17def-e994-42d5-a95c-eccd2049bf6c 500 Sanz Sánchez, Fernando 120bd4b152bf1bd9 600 0000-0001-6455-5986 2024-06-17T21:32:43Z 2024-06-17T21:32:43Z 2021 Rev. Mat. Iberoam. 38 (2022), no. 5, 1501–1527 0213-2230 https://uvadoc.uva.es/handle/10324/68129 10.4171/RMI/1311 1501 5 1527 Revista Matemática Iberoamericana 38 2235-0616 Producción Científica 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. F. Sanz Sánchez was partially supported by Ministerio de Ciencia, Spain, process MTM2016-77642-C2-1-P and PID2019-105621GB-I00 application/pdf eng European Mathematical Society Press info:eu-repo/semantics/restrictedAccess Real Sociedad Matemática Española solutions of ODEs, non-oscillating trajectories of vector fields, o-minimality, Hardy field, transcendental formal solutions Solutions of definable ODEs with regular separation and dichotomy interlacement versus Hardy info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion SI THUMBNAIL 2021_LeG-Mat-San_Rev-Ib-Mat.pdf.jpg 2021_LeG-Mat-San_Rev-Ib-Mat.pdf.jpg IM Thumbnail image/jpeg 1744 https://uvadoc.uva.es/bitstream/10324/68129/3/2021_LeG-Mat-San_Rev-Ib-Mat.pdf.jpg e15284c0db759f7b3648d2548b2ddc84 MD5 3 LICENSE license.txt license.txt text/plain 3929 https://uvadoc.uva.es/bitstream/10324/68129/2/license.txt 289d98c1665ee0d20312360f0e8643c8 MD5 2 ORIGINAL 2021_LeG-Mat-San_Rev-Ib-Mat.pdf 2021_LeG-Mat-San_Rev-Ib-Mat.pdf application/pdf 483755 https://uvadoc.uva.es/bitstream/10324/68129/1/2021_LeG-Mat-San_Rev-Ib-Mat.pdf bc34a77ae7a05b30c980ef618f03e292 MD5 1 10324/68129 oai:uvadoc.uva.es:10324/68129 2024-12-03 15:36:52.846 UVaDOC repositorio@uva.es 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