Galina Filipuk, University of Warsaw
title: Nonlinear differential equations and the geometric approach.
´¡²ú²õ³Ù°ù²¹³¦³Ù:ÌýNonlinear differential equations may have complicated singularities in the complex plane. Painleve equations are nonlinear second order differential equations solutions of which have no movable critical points. They have a lot of nice properties. The quasi-Painleve equations admit algebraic branch points. The geometric approach to the Painleve equations was developed in the works of K. Okamoto, H. Sakai and many others. In thisvtalk I shall present some recent results using the geometric approach (including, if time permits, the general procedure of the reduction of recurrence coefficients of semi-classical orthogonal polynomials to the Painleve equations as an example of the solution of the so-called Painleve equivalence problem, equations with the algebro-Painleve property, equations with the quasi-Painleve property, Lienard type equations and so on). This talk is based on several published papers and preprints joint with A. Dzhamay, A. Ligeza, A. Stokes and T. Kecker.
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