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2024-06-21T09:34:41Z urn:hdl:10324/68174 Trajectories in interlaced integral pencils of 3-dimensional analytic vector fields are o-minimal Le Gal, Olivier Sanz Sánchez, Fernando Speissegger, Patrick Let ξ be an analytic vector field at (R3, 0) and I be an analytically non-oscillatory integral pencil of ξ; i.e., I is a maximal family of analytically non-oscillatory trajectories of ξ at 0 all sharing the same iterated tangents. We prove that if I is interlaced, then for any trajectory Γ ∈ I, the expansion Ran,Γ of the structure Ran by Γ is model-complete, o-minimal and polynomially bounded. 2024-06-21T09:34:41Z 2024-06-21T09:34:41Z 2017 info:eu-repo/semantics/article TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 370, Number 3, March 2018, Pages 2211–2229 0002-9947 https://uvadoc.uva.es/handle/10324/68174 10.1090/tran/7205 2211 3 2229 Transactions of the American Mathematical Society 370 1088-6850 spa info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional