An Asymptotic Reduction of a Painleve' VI equation to a Painleve' III   (January 2011)
  When the independent variable is close to a critical point, it is shown that PVI can be asymptotically reduced to PIII. In this way, it is possible to compute the leading term of the critical behaviors of PVI transcendents starting from the behaviors of PIII transcendents. 
Davide Guzzetti
math.CA