Abstract
Let ξ be an analytic vector field in R3 with 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 π of the local invariant 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 Fr(Vn) is everywhere tangent to ξ except around Fr(Vn)∩Λ, where transversality is mandatory.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
