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math.DS2021
Explicit rank-one constructions for irrational rotations
Alexandre I. Danilenko, Mykyta I. Vieprik
For each {\it well approximable} irrational , we provide an explicit rank-one construction of the -rotation on the circle . This solves "almost surely" a…
math.DS2021
Krieger's type for ergodic nonsingular Poisson actions of non-(T) locally compact groups
Alexandre I. Danilenko
It is shown that each non-compact locally compact second countable non-(T) group possesses non-strongly ergodic weakly mixing IDPFT Poisson actions of arbitrary Krieger's type.…
math.DS2021
Haagerup property and Kazhdan pairs via ergodic infinite measure preserving actions
Alexandre I. Danilenko
It is shown that a locally compact second countable group has the Haagerup property if and only if there exists a sharply weak mixing 0-type measure preserving free -action…