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A note on limit laws for minimal Cantor systems with infinite periodic spectrum

• Recently in [6] Y. Lacroix proved that any distribution function can be obtained as a limit law of return time for any ergodic aperiodic system. In this note we provide an alternative construction, based on Bratteli-Vershik representations of systems, which works for any minimal Cantor system having an infinite periodic spectrum. The construction is especially simple for odometers.
Mathematics Subject Classification: Primary: 54H20; Secondary: 37B20.

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