Closed characteristics on compact convex hypersurfaces in R8

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Focusing on Hamiltonian analysis, the research presents a solution to a longstanding conjecture for the n=4 case by employing Morse theory and the index iteration theory for symplectic paths. It introduces a novel commutative property for closed characteristics, contributing to the understanding of closed characteristics on compact convex hypersurfaces in R8. This work is a reprint from Advances in Mathematics, showcasing significant findings in the field.