2,610 research outputs found
Poles Distribution of PVI Transcendents close to a Critical Point (summer 2011)
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.Comment: 35 pages, 10 figures; Physica D (2012
Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces
We compute Stokes matrices and monodromy for the quantum cohomology of
projective spaces. We prove that the Stokes' matrix of the quantum cohomology
coincides with the Gram matrix in the theory of derived categories of coherent
sheaves.Comment: 50 pages, 6 Postscript figure
Solving the Sixth Painleve' Equation: Towards the Classification of all the Critical Behaviours and the Connection Formulae (October 2010)
The critical behavior of a three real parameter class of solutions of the
sixth Painlev\'e equation is computed, and parametrized in terms of monodromy
data of the associated matrix linear Fuchsian system of ODE. The
class may contain solutions with poles accumulating at the critical point. The
study of this class closes a gap in the description of the transcendents in one
to one correspondence with the monodromy data. These transcendents are reviewed
in the paper. Some formulas that relate the monodromy data to the critical
behaviors of the four real (two complex) parameter class of solutions are
missing in the literature, so they are computed here. A computational procedure
to write the full expansion of the four and three real parameter class of
solutions is proposed.Comment: 53 pages, 2 figure
Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)
The critical and asymptotic behaviors of solutions of the sixth Painlev\'e
equation PVI, obtained in the framework of the monodromy preserving deformation
method, and their explicit parametrization in terms of monodromy data, are
tabulated.Comment: 30 pages, 1 figure; Nonlinearity 201
Inverse Problem for semisimple Frobenius Manifolds, Monodromy Data and the Painleve' VI Equation
We study critical behaviour and connection problem for a Painleve' 6
equation. We construct solutions of WDVV eqs. using the isomonodromic
deformation method and the Painleve' equations. We find algebraic solutions of
WDVV and Gromov-Witten invariants of projective space.Comment: 131 pages 16 figure
Notes on non-generic isomonodromy deformations
Some of the main results of [Cotti G., Dubrovin B., Guzzetti D., Duke Math. J., to appear, arXiv:1706.04808], concerning non-generic isomonodromy deformations of a certain linear differential system with irregular singularity and coalescing eigenvalues, are reviewed from the point of view of Pfaffian systems, making a distinction between weak and strong isomonodromic deformations. Such distinction has a counterpart in the case of Fuchsian systems, which is well known as Schlesinger and non-Schlesinger deformations, reviewed in Appendix A
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