Periodic orbits of Linear flows on connected Lie groups
DOI:
https://doi.org/10.22199/issn.0717-6279-5261Keywords:
periodic orbits, linear flows, connected Lie groupsAbstract
Our main goal is to study the periodic orbits of linear flows on a real, connected Lie group. Since each linear flow φt has a derivation associated 𝒟, we show that the existence of periodic orbits of φt is based on the eigenvalues of the derivation 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 a connected, simply connected, solvable Lie groups of dimension 2 or 3.
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