912 research outputs found
Transformations of the Ranks and Algebraic Solutions of the Sixth Painlev\'e Equation
Compositions of rational transformations of independent variables of linear
matrix ordinary differential equations (ODEs) with the Schlesinger
transformations (-transformations) are used to construct algebraic
solutions of the sixth Painlev\'e equation. -Transformations of the ranks 3
and 4 of matrix Fuchsian ODEs with 3 singular points into analogous
ODE with 4 singular points are classified.Comment: 26 page
Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlev\'{e} Equation. I
The degenerate third Painlev\'{e} equation, , where ,
and , and the associated tau-function are studied via the
Isomonodromy Deformation Method. Connection formulae for asymptotics of the
general as and solution and general regular as and solution are obtained.Comment: 40 pages, LaTeX2
Computation of highly ramified coverings
An almost Belyi covering is an algebraic covering of the projective line,
such that all ramified points except one simple ramified point lie above a set
of 3 points of the projective line. In general, there are 1-dimensional
families of these coverings with a fixed ramification pattern. (That is,
Hurwitz spaces for these coverings are curves.) In this paper, three almost
Belyi coverings of degrees 11, 12, and 20 are explicitly constructed. We
demonstrate how these coverings can be used for computation of several
algebraic solutions of the sixth Painleve equation.Comment: 26 page
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