Secants of trajectories in dimension three
In this paper we give a description of the sets of accumulation of secants for orbits of real analytic vector fields in dimension three with the origin as only ω-limit point. It is an infinitesimal version of the Poincaré-Bendixson problem in dimension three. These sets have structure of cyclic graph when the singularities are isolated under one blow-up. If the reduction of singularities is hyperbolic, under conditions of Morse-Smale type, we prove that the accumulation set is a single point or homeomorphic to ?1.
Autor(es):Alonso, Clementa
Cano, Felipe
Rosas, Rudy
Año: 2013
Título de la revista: Progress and Challenges in Dynamical Systems. Springer Proceedings in Mathematics & Statistics.
Volumen: 54
Página inicial - Página final: 1-6
Url: https://link.springer.com/chapter/10.1007/978-3-642-38830-9_1