RT info:eu-repo/semantics/article
T1 Stratification of three-dimensional real flows I: Fitting domains
A1 Alonso-González, C.
A1 Sanz Sánchez, F.
K1 Real vector fields; Singularities; Foliations; Reduction of singularities; Vector fields dynamics
AB Let ξ be an analytic vector field in R3with an isolated singularity at the origin and having only hyperbolic singular points after a reduction of singularities π:M→R3. The union of the images by πof the local invariant manifolds at those hyperbolic points, denoted by  , is composed of trajectories of ξ accumulating to 0 ∈R3. Assuming that there are no cycles nor polycycles on the divisor of π, together with a Morse-Smale type property and a non-resonance condition on the eigenvalues at these points, in this paper we prove the existence of a fundamental system {Vn}of neighborhoods well adapted for the description of the local dynamics of ξ: the frontier Fr(Vn) is everywhere tangent to ξexcept around Fr(Vn) ∩ , where transversalityis mandatory.
PB Elsevier
SN 0022-0396
YR 2023
FD 2023
LK https://uvadoc.uva.es/handle/10324/68106
UL https://uvadoc.uva.es/handle/10324/68106
LA eng
NO Journal of Differential Equations, 361 (2023), p. 40–96
DS UVaDOC
RD 06-ago-2024