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It is well known from the quantum theory of strongly correlated systems thatpoles (or more subtle singularities) of dynamic correlation functions incomplex plane usually correspond to the collective or localized modes. Here weaddress singularities of velocity autocorrelation function $Z$ in complex$\omega$-plain for the one-component particle system with isotropic pairpotential. We have found that naive few poles picture fails to describeanalytical structure of $Z(\omega)$ of Lennard-Jones particle system in complexplain. Instead of few isolated poles we see the singularity manifold of$Z(\omega)$ forming branch cuts that suggests Lennard-Jones velocityautocorrelation function is a multiple-valued function of complex frequency.The brunch cuts are separated from the real axis by the well-defined "gap". Thegap edges extend approximately parallel to the real frequency axis. Thesingularity structure is very stable under increase of the temperature; we havefound its trace at temperatures even several orders of magnitude higher thanthe melting point. Our working hypothesis that the branch cut origin is relatedto the "interference" in $Z$ of one-particle kinetics and collectivehydrodynamic motion.

Singularity band of velocity auto correlation function of Lennard-Jones fluid in complex $\omega$-plain