RT info:eu-repo/semantics/article
T1 Stratification of three-dimensional real flows I: Fitting domains
A1 Alonso González, C.
A1 Sanz Sánchez, Fernando
K1 Matemáticas
K1 Geometría
K1 Real vector fields
K1 Singularities
K1 Foliations
K1 Campos vectoriales reales
K1 Singularidades
K1 Foliaciones
K1 12 Matemáticas
K1 1204 Geometría
AB Let ξ be an analytic vector field in R3 with an isolated singularity at the origin and having only hyperbolicsingular points after a reduction of singularities π : M → R3. The union of the images by π of the localinvariant manifolds at those hyperbolic points, denoted by Λ, 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 F r(Vn) is everywhere tangent to ξ except around F r(Vn) ∩ Λ, where transversality is mandatory.
PB Elsevier
SN 0022-0396
YR 2023
FD 2023
LK https://uvadoc.uva.es/handle/10324/58920
UL https://uvadoc.uva.es/handle/10324/58920
LA eng
NO Journal of Differential Equations, 2023, vol. 361, p. 40-96
NO Producción Científica
DS UVaDOC
RD 27-jul-2024