TY - JOUR

T1 - On isomorphism problem for von Neumann flows with one discontinuity

AU - Kanigowski, Adam

AU - Solomko, Anton V.

PY - 2018/5/11

Y1 - 2018/5/11

N2 - A von Neumann flow is a special flow over an irrational rotation of the circle and under a piecewise C1 roof function with a non-zero sum of jumps. We prove that the absolute value of the jump 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 if the jumps of the roof functions have different absolute values, regardless of the irrational rotation in the base.

AB - A von Neumann flow is a special flow over an irrational rotation of the circle and under a piecewise C1 roof function with a non-zero sum of jumps. We prove that the absolute value of the jump 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 if the jumps of the roof functions have different absolute values, regardless of the irrational rotation in the base.

UR - http://www.scopus.com/inward/record.url?scp=85046773556&partnerID=8YFLogxK

U2 - 10.1007/s11856-018-1701-5

DO - 10.1007/s11856-018-1701-5

M3 - Article (Academic Journal)

AN - SCOPUS:85046773556

SP - 1

EP - 18

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -