A non-Borel special alpha-limit set in the square

@article{65306,
   author = {Jackson, Stephen and Mance, Bill and Roth, Samuel Joshua},
   article_location = {New York},
   article_number = {8},
   doi = {http://dx.doi.org/10.1017/etds.2021.68},
   keywords = {special alpha limit set; triangular map of the square; non-Borel analytic set},
   language = {eng},
   issn = {0143-3857},
   journal = {Ergodic Theory and Dynamical Systems},
   title = {A non-Borel special alpha-limit set in the square},
   url = {https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/nonborel-special-alphalimit-set-in-the-square/48C7F0D48DC9D31458F7ED63ED195AC1},
   volume = {42},
   year = {2022}
}

TY  - JOUR
ID  - 65306
AU  - Jackson, Stephen - Mance, Bill - Roth, Samuel Joshua
PY  - 2022
TI  - A non-Borel special alpha-limit set in the square
JF  - Ergodic Theory and Dynamical Systems
VL  - 42
IS  - 8
SP  - 2550-2560
EP  - 2550-2560
PB  - Cambridge University Press
SN  - 01433857
KW  - special alpha limit set
KW  - triangular map of the square
KW  - non-Borel analytic set
UR  - https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/nonborel-special-alphalimit-set-in-the-square/48C7F0D48DC9D31458F7ED63ED195AC1
N2  - 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.
ER  - 

JACKSON, Stephen, Bill MANCE and Samuel Joshua ROTH. A non-Borel special alpha-limit set in the square. \textit{Ergodic Theory and Dynamical Systems}. New York: Cambridge University Press, 2022, vol.~42, No~8, p.~2550-2560. ISSN~0143-3857. Available from: https://dx.doi.org/10.1017/etds.2021.68.