Trajectories in interlaced integral pencils of 3-dimensional analytic vector fields are o-minimal

2013/10/08 by Olivier Le Gal, Gal, Olivier Le, Fernando Sanz +3
Mathematics · Physics and Astronomy · #03C64 #34C08 #34M30 #Advanced Differential Equations and Dynamical Systems #Advanced Operator Algebra Research #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Logic (math.LO) #Nonlinear Differential Equations Analysis #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1310.2225

openalex publication_date 2013/10/08 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Let X be an analytic vector field defined in a neighborhood of the origin of R³, and let I be an analytically non-oscillatory integral pencil of X; that is, I is a maximal family of analytically non-oscillatory trajectories of X at the origin all sharing the same iterated tangents. We prove that if I is interlaced, then for any trajectory T in I, the expansion of the structure generated over the real field by T and all globally subanalytic sets is model-complete, o-minimal and polynomially bounded.

Citations

• Geometric categories and o-minimal structures

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