Abstract
A relation between a canonical set of integrals of motion and the Lepagean (fundamental) differential form theta in higher-order mechanics is studied. The canonical set of integrals of motion is introduced as a system of functions of coordinates, time and higher-order velocities of the given mechanical system, satisfying certain axioms of functional independence, completeness and canonical adjointness. It is shown that there exists a correspondence between canonical sets of integrals of motion and semiregular Lepagean forms. A connection of invariance transformations of the form d theta with integrals of motion is studied, and a generalisation of the local Liouville theorem on the integrals of motion in involution is given.
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