Infinitesimal Poincaré-Bendixson problem in dimension 3
We describe the sets of accumulation of secants for orbits of real analytic vector fields in dimension 3 having the origin as only ω-limit point. It is a kind of infinitesimal Poincaré–Bendixson problem in dimension 3. These sets have structure of a cyclic graph when the singularities are isolated under one blow-up. In the case of hyperbolic reduction of singularities with conditions of Morse–Smale-type, we prove that the accumulation set is at most a single poly-cycle isomorphic to S1.
Autor(es):Alonso, Clementa
Cano, Felipe
Rosas, Rudy
Año: 2014
Título de la revista: International Mathematics Research Notices
Volumen: 21
Número: 1
Página inicial - Página final: 5994–6019
ISSN: 1073-7928
Url: https://academic.oup.com/imrn/article/2014/21/5994/726080