Examples of infinitesimal non-trivial accumulation of secants in dimension three

Abstract

We present non-trivial examples of accumulation of secants for orbits (of real analytic three dimensional vector fields) having the origin as only $\omega$-limit point. These non-trivial sets have the structure of a proper algebraic variety of ${\mathbb{S}}^2$ intersected with a cone.

Journal of Dynamical and Control Systems, 2014

References in corpus (2)

• Analytic varieties as limit periodic sets
• Infinitesimal Poincaré-Bendixson Problem in dimension three