Periodic orbits of Linear flows on connected Lie groups

• Stelmastchuk, Simão Nicolau ^[1]
  1. [1] Universidade Federal do Paraná

     Universidade Federal do Paraná

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 3, 2023, págs. 663-680
• Idioma: inglés
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• Resumen

  • 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.