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Abstract
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One of the most important questions about the existence of integrable geodesic
flows on the torus are still unsolved. Bolsinov, Fomenko and Kozlov in the review
article stated a conjecture about the integrable systems that have a linear and
quadratic integral on some two dimensional surfaces. In this article we try to state
and extend some methods to solve a problem on torus and use the geodesic flows
to classification of integrable systems in a potential fields on torus as a surface of
revolution.
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