@article{45a697bf7d1b4df28fc4925ab13b01fa,
title = "Exceptional solutions to the Painlev{\'e} VI equation",
abstract = "We find all solutions of the Painlev{\'e} VI equations with the property that they have no zeros, no poles, no 1-points, and no fixed points.",
author = "Alexandre Eremenko and Andrei Gabrielov and Aimo Hinkkanen",
note = "Funding Information: We thank Chang-Shou Lin who sent us his work2 and communicated solution (2) before Ref. 3 was released, Clifford Earle for showing us an unpublished letter of Carleson with an elementary proof of Theorem A, and the referee for bringing Ref. 1 to our attention. We also thank Oleg Lisovyy, T. N. Venkataramana, and Math Overflow participants6 for illuminating discussions. Supported by NSF Grant Nos. DMS-1361836 and DMS-1161629.",
year = "2017",
month = jan,
day = "1",
doi = "10.1063/1.4973440",
language = "English (US)",
volume = "58",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "1",
}