Poles Distribution of PVI Transcendents close to a Critical Point (summer 2011)

Abstract

The distribution of the poles of branches of the Painleve' VI transcendents associated to semi-simple Frobenius manifolds is determined close to a critical point. It is shown that the poles accumulate at the critical point, asymptotically along two rays. The example of the Frobenius manifold given by the quantum cohomology of the two-dimensional complex projective space is also considered.

35 pages, 10 figures; Physica D (2012)

References in corpus (2)

• Matching Procedure for the Sixth Painlevé Equation (May 2006)
• On the Logarithmic Asymptotics of the Sixth Painleve' Equation (Summer 2007)

Cited by in corpus (5)

• A Review on The Sixth Painleve' Equation
• Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)
• A Riemann-Hilbert Approach to the Heun Equation
• Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I
• On the convergence of exotic formal series solutions of an ODE. A proof by the implicit mapping theorem