# Periodic orbits of Linear and Invariant flows on Semisimple Lie groups

@article{Stelmastchuk2020PeriodicOO, title={Periodic orbits of Linear and Invariant flows on Semisimple Lie groups}, author={Sim{\~a}o Stelmastchuk}, journal={arXiv: Dynamical Systems}, year={2020} }

Our main is to study periodic orbits of linear or invariant flows on a real, connected, semisimple Lie group. Since there exist a derivation of Lie algebra to linear or invariant flow, we show that a periodic orbit that is not fixed point of a linear or invariant flow is periodic if and only the eingevalues of derivation is 0 or $\pm \alpha i$ for an unique $\alpha \neq 0$ and they are semisimple. We apply this result in noncompact case through Iwasawa's decomposition. Furthermore, we present a…

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