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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Yu. E. Gliklikh},
     title = {An operator approach to periodic solutions of differential equations on lie groups},
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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/