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non-borel analytic set

Ergodic Theory and Dynamical Systems (1)

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A non-Borel special alpha-limit set in the square
Part of
STEPHEN JACKSON, BILL MANCE, SAMUEL ROTH
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 8 / August 2022

Published online by Cambridge University Press:

22 July 2021, pp. 2550-2560

Print publication:

August 2022
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We consider the complexity of special $\alpha $ -limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necessarily Borel, even in the case of a surjective map on the unit square. This answers a question posed by Kolyada, Misiurewicz, and Snoha.