 A. N. Livšic

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.^[ref][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.^[ref]