Computational Mathematics

An operator approach to periodic solutions of differential equations on lie groups

Yu. E. Gliklikh<sup>ab

a</sup> Voronezh State University, Voronezh, Russian Federation
^b South Ural State University, Chelyabinsk, Russian Federation

Abstract: 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.

UDC: 517.9

Received: 18.04.2022

Language: English

DOI: 10.14529/jcem220202

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