Geodesic
Turning points of linear systems and double asymptotics of the Painlevé transcendents
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 53-74 Cet article a éte moissonné depuis la source Math-Net.Ru

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On a base of the connection between the theories of linear and nonlinear special functions the method which allow one to consider the well-known formal limits from more complicated Painlevé equations to the less ones as the double asymptotics of the concrete solutions of these equations is found. The hierarchies of the first and second Painlevé equations are found to be the special functions which describe the isomonodromy collidence of the turning points in linear systems of ordinary differential equations. 
@article{ZNSL_1991_187_a3,
     author = {A. V. Kitaev},
     title = {Turning points of linear systems and double asymptotics of the {Painlev\'e} transcendents},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {53--74},
     year = {1991},
     volume = {187},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a3/}
}
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A. V. Kitaev. Turning points of linear systems and double asymptotics of the Painlevé transcendents. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 53-74. http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a3/