= A. N. Livšic
{c}
<A. N. Livšic> authored the 1972 paper Cohomology of dynamical systems, associated with the <Livšic theorem>. The original publication record and later primary research references verify these initials; they are retained without inferring a fuller personal identity.https://doi.org/10.1070/IM1972v006n06ABEH001919[Original paper, Mathematics of the USSR-Izvestiya 6(6), 1278–1301]{ref}<Abelian Livšic theorems for Anosov flows by Richard Sharp>[Reference 17, original Russian publication record]{ref}
For an equation $u\circ T-u=f$, summing along a <periodic orbit> telescopes to zero. Thus periodic sums of $f$ must vanish. Livšic theory shows that, in suitable hyperbolic settings with the required regularity assumptions, this necessary periodic-orbit test also yields a transfer function. The result turns infinitely many local orbit checks into a global solution of a <cohomological equation>.<Abelian Livšic theorems for Anosov flows by Richard Sharp>[Introduction, classical Livšic framework]{ref}
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