On the monodromy of the deformed cubic oscillator
Keyword(s):
AbstractWe study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlevé equation. We use the generalised monodromy map for this equation to give solutions to the Riemann-Hilbert problems of (Bridgeland in Invent Math 216(1):69–124, 2019) arising from the Donaldson-Thomas theory of the A$$_2$$ 2 quiver. These are the first known solutions to such problems beyond the uncoupled case. The appendix by Davide Masoero contains a WKB analysis of the asymptotics of the monodromy map.
1993 ◽
Vol 118
(3)
◽
pp. 813-813
◽
1986 ◽
Vol 102
(3-4)
◽
pp. 253-257
◽
2018 ◽
Vol 973
◽
pp. 012057
◽
1965 ◽
Vol 14
(3)
◽
pp. 327-334
◽
1987 ◽
Vol 123
(2)
◽
pp. 366-375
1963 ◽
Vol 27
(3)
◽
pp. 847-861
2014 ◽
Vol 57
◽
pp. 44-59
◽
1949 ◽
Vol 35
(4)
◽
pp. 190-191
◽