TY - JOUR
T1 - Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I
AU - Chen, Zhijie
AU - Kuo, Ting Jung
AU - Lin, Chang Shou
PY - 2017/6/1
Y1 - 2017/6/1
N2 - In this paper, we study the Painlevé VI equation with parameter (98,−18, 18, 38). We prove (i) An explicit formula to count the number of poles of an algebraic solution with the monodromy group of the associated linear ODE being DN, where DN is the dihedral group of order 2N. (ii) There are only four solutions without poles in C∖{0,1}. (iii) If the monodromy group of the associated linear ODE of a solution λ(t) is unitary, then λ(t) has no poles in R∖{0,1}.
AB - In this paper, we study the Painlevé VI equation with parameter (98,−18, 18, 38). We prove (i) An explicit formula to count the number of poles of an algebraic solution with the monodromy group of the associated linear ODE being DN, where DN is the dihedral group of order 2N. (ii) There are only four solutions without poles in C∖{0,1}. (iii) If the monodromy group of the associated linear ODE of a solution λ(t) is unitary, then λ(t) has no poles in R∖{0,1}.
KW - Algebraic solution
KW - Painlevé VI equation
KW - Pole distribution
UR - http://www.scopus.com/inward/record.url?scp=85011632800&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85011632800&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2017.01.016
DO - 10.1016/j.geomphys.2017.01.016
M3 - Article
AN - SCOPUS:85011632800
SN - 0393-0440
VL - 116
SP - 52
EP - 63
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -