Geodesic
An operator approach to periodic solutions of differential equations on lie groups
Journal of computational and engineering mathematics, Tome 9 (2022) no. 2, pp. 21-25

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The machinery of integral operators with parallel translation is elaborated such that for a $T$-periodic ordinary differential equation (i.e., a vector field) on a Lie group with continuous right-hand side the fixed points of those operators are $T$-periodic solutions. It is shown that under some natural conditions the second iteration of such operator is completely continuous.
Keywords: Lie groups, ordinary differential equations, integral operators with parallel translation, periodic solutions. 
Yu. E. Gliklikh. An operator approach to periodic solutions of differential equations on lie groups. Journal of computational and engineering mathematics, Tome 9 (2022) no. 2, pp. 21-25. http://geodesic.mathdoc.fr/item/JCEM_2022_9_2_a1/
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     title = {An operator approach to periodic solutions of differential equations on lie groups},
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