Linear flows on compact, semisimple Lie groups: stability, periodic orbits, and Poincaré-Bendixon's Theorem

2018/06/21 by Stelmastchuk, S. N.
#22E46 #37C10 #37C27 #37C75 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.08026

Abstract

Our first purpose is to study the stability of linear flows on real, connected, compact, semisimple Lie groups. After, we study and classify periodic orbits of linear and invariant flows. In particular, we obtain a version of Poincaré-Bendixon's Theorem. As an application, we present periodic orbits of linear or invariant flows on SO(3) or SU(2), and we classify periodic orbits of a linear or invariant system on SO(4).

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