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GENERALIZED MONODROMY DATA
"... ABSTRACT. In this note, we will give a brief summary of geometric approach to understanding equations of Painlev\’e type ( $[0] $ , [Sakai], [STT], [IISI], [In]). Finally, we report the recent result on the moduli space of the generalized monodromy data associated to 10 families of isomonodromic pro ..."
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ABSTRACT. In this note, we will give a brief summary of geometric approach to understanding equations of Painlev\’e type ( $[0] $ , [Sakai], [STT], [IISI], [In]). Finally, we report the recent result on the moduli space of the generalized monodromy data associated to 10 families of isomonodromic
Monodromydata parametrization of
, 2005
"... spaces of local solutions of integrable reductions of Einstein’s field equations ..."
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spaces of local solutions of integrable reductions of Einstein’s field equations
Inverse Problem for Semisimple Frobenius Manifolds Monodromy Data and the Painlevé VI Equation
, 2000
"... This work is a part the Ph.D. thesis of Davide Guzzetti, with the supervision of professor B. Dubrovin. We study the inverse problem for semisimple Frobenius manifolds of dimension three. We explicitly compute a parametric form of the solutions of the WDVV equations of associativity in terms of solu ..."
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of solutions of a special Painlevé VI equation and we show that the solutions are labelled by a set of monodromy data. The procedure is a relevant application of the theory of isomonodromic deformations. We use the parametric form to construct polynomial and algebraic solutions of the WDVV equations. We also
DIRECT COMPUTATION OF THE MONODROMY DATA FOR P6 CORRESPONDING TO THE QUANTUM COHOMOLOGY OF THE PROJECTIVE PLANE
"... Abstract. A solution to the sixth Painleve equation (P6) corresponding to the quantum cohomology of the projective plane QH ∗ (C 2) (see work by Manin [19]) is considered. This is one of the solutions to P6 coming from the Frobenius manifold theory (see [10]). The resulting generators of the monodro ..."
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of the monodromy group are computed. The main difference in the author’s approach is its directness, so that no references to the Frobenius manifold theory are needed. The proof presented in the article requires only a) classical results on the asymptotic expansion of some special cases of the hypergeometric
Black Hole Monodromy and Conformal Field Theory
, 2013
"... The analytic structure of solutions to the KleinGordon equation in a black hole background, as represented by monodromy data, is intimately related to black hole thermodynamics. It encodes the ''hidden conformal symmetry'' of a nonextremal black hole, and it explains why featur ..."
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The analytic structure of solutions to the KleinGordon equation in a black hole background, as represented by monodromy data, is intimately related to black hole thermodynamics. It encodes the ''hidden conformal symmetry'' of a nonextremal black hole, and it explains why
Gravitational Solitons and Monodromy Transform Approach to Solution of Integrable Reductions of Einstein Equations
, 1999
"... In this paper the well known Belinskii and Zakharov soliton generating transformations of the solution space of vacuum Einstein equations with twodimensional Abelian groups of isometries are considered in the context of the so called ”monodromy transform approach”, which provides some general base ..."
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for the study of various integrable space time symmetry reductions of Einstein equations. Similarly to the scattering data used in the known spectral transform, in this approach the monodromy data for solution of associated linear system characterize completely any solution of the reduced Einstein equations
Monodromy of an Inhomogeneous PicardFuchs Equation
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2012
"... The global behaviour of the normal function associated with van Geemen’s family of lines on the mirror quintic is studied. Based on the associated inhomogeneous Picard–Fuchs equation, the series expansions around large complex structure, conifold, and around the open string discriminant are obtaine ..."
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Cited by 1 (0 self)
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are obtained. The monodromies are explicitly calculated from this data and checked to be integral. The limiting value of the normal function at large complex structure is an irrational number expressible in terms of the dilogarithm.
Eigenvalues for the monodromy of the Milnor fibers of arrangements Trends
 in Singularities, 141150, 2002 Birkhauser Verlag
"... We decribe upper bounds for the orders of the eigenvalues of the monodromy of Milnor fibers of arrangements given in terms of combinatorics. 1 Introduction. still can be easily calculated by A’Campo method, the eigenvalues of Tf,i for each i reflect more subtle properties of the singularity not nece ..."
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Cited by 23 (1 self)
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We decribe upper bounds for the orders of the eigenvalues of the monodromy of Milnor fibers of arrangements given in terms of combinatorics. 1 Introduction. still can be easily calculated by A’Campo method, the eigenvalues of Tf,i for each i reflect more subtle properties of the singularity
Monodromy transform approach to solution of some field equations in General Relativity and string heory”, Proceedings of the workshop ”Nonlinearity, Integrability and all that: Twenty years after NEEDS’79
 12 – 18, World Scientific, Singapore (2000); grqc/9911045
, 1999
"... A monodromy transform approach, presented in this communication, provides a general base for solution of spacetime symmetry reductions of Einstein equations in all known integrable cases, which include vacuum, electrovacuum, massless Weyl spinor field and stiff fluid, as well as some string theory ..."
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Cited by 4 (3 self)
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induced gravity models. There were found a special finite set of functional parameters which are defined as the set of monodromy data for the fundamental solution of associated spectral problem. These monodromy data consist of the functions of the spectral parameter only. Similarly to the scattering data
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