TY - JOUR
T1 - The third, fifth and sixth painlevé equations on weighted projective spaces
AU - Chiba, Hayato
N1 - Publisher Copyright:
© 2015, Institute of Mathematics. All rights reserved.
PY - 2016/2/23
Y1 - 2016/2/23
N2 - The third, fifth and sixth Painlevé equations are studied by means of the weighted projective spaces CP3(p, q, r, s) with suitable weights (p, q, r, s) determined by the Newton polyhedrons of the equations. Singular normal forms of the equations, symplectic atlases of the spaces of initial conditions, Riccati solutions and Boutroux's coordinates are systematically studied in a unified way with the aid of the orbifold structure of CP3(p, q, r, s) and dynamical systems theory.
AB - The third, fifth and sixth Painlevé equations are studied by means of the weighted projective spaces CP3(p, q, r, s) with suitable weights (p, q, r, s) determined by the Newton polyhedrons of the equations. Singular normal forms of the equations, symplectic atlases of the spaces of initial conditions, Riccati solutions and Boutroux's coordinates are systematically studied in a unified way with the aid of the orbifold structure of CP3(p, q, r, s) and dynamical systems theory.
KW - Painlevé equations
KW - Weighted projective space
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U2 - 10.3842/SIGMA.2016.019
DO - 10.3842/SIGMA.2016.019
M3 - Article
AN - SCOPUS:84959241297
SN - 1815-0659
VL - 12
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
M1 - 019
ER -