Stratification of three-dimensional real flows I: Fitting domains

Let ξ be an analytic vector field in R3 with isolated singularity at the origin and having only hyperbolic singular points after a reduction of singularities π:M→R3. The union images by π local invariant manifolds those points, denoted Λ, is composed trajectories accumulating to 0∈R3. Assuming that there are no cycles nor polycycles on divisor π, together Morse-Smale type property non-resonance condition eigenvalues these this paper we prove existence fundamental system {Vn} neighborhoods well adapted for description dynamics ξ: frontier Fr(Vn) everywhere tangent except around Fr(Vn)∩Λ, where transversality mandatory.