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A von Neumann flow is a special flow over an irrational rotation of thecircle and under a piecewise $C^1$ roof function with a non-zero sum of jumps.We prove that the absolute value of the slope is a (measure theoretic)invariant in the class of von Neumann special flows with one discontinuity,i.e. two ergodic von Neumann flows with one discontinuity are not isomorphic ifthe slopes of the roof functions have different absolute values, regardless ofthe irrational rotation in the base.

On isomorphism problem for von Neumann flows with one discontinuity