Periodic orbits of Linear flows on connected Lie groups
Our main is to study periodic orbits of linear flows on a real, connected Lie group. Since each linear flow $\varphi_t$ has a derivation associated $\mathcal{D}$, we show that the existence of periodic orbits of $\varphi_t$ is in the function of the eigenvalues of derivation $\mathcal{D}$. From this, we study periodic orbits of a linear flow on noncompact, semisimple Lie groups, and we work with periodic orbits of a linear flow on connected Lie groups of dimension 2 or 3.
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Dynamical Systems