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We find a class of solutions of the sixth Painleve' equation appearing in thetheory of WDVV equations. This class covers almost all the monodromy dataassociated to the equation, except one point in the space of the data. We findthe critical behavior close to the critical points in terms of two parametersand solve the connection problem.  We also study the critical behavior of Painleve' transcendents in theElliptic representation.

On the Critical Behavior, the Connection problem and the Elliptic representation of a Painleve VI equation (Spring 2001)