Infinitesimal Poincaré Bendixson problem in dimension three
Alonso-González, C.; Cano, F.; Rosas, R.
Intenational Mathematics Research Notices 21 (2014), 5994-6019.
doi = {10.1093/imrn/rnt154}
abstract ={We describe the sets of accumulation of secants for orbits of real analytic vector fields in dimension 3 having the origin as only ?-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 .},
URL = {http://imrn.oxfordjournals.org/content/early/2013/07/19/imrn.rnt154.abstract},
eprint = {http://imrn.oxfordjournals.org/content/early/2013/07/19/imrn.rnt154.full.pdf+html},