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arXiv · 2002.08479

Periodic orbits of Linear and invariant flows on connected Lie groups

S. N. Stelmastchuk
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Abstract

Our main is to study periodic orbits of linear and invariant 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 based on the eigenvalues of the 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, simply connected, solvable Lie groups of dimension 2 or 3.

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S. N. Stelmastchuk. 2020-02-19. Periodic orbits of Linear and invariant flows on connected Lie groups. https://arxiv.org/abs/2002.08479

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