Relevant bibliographies by topics / Isomonodromic deformations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Isomonodromic deformations'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Isomonodromic deformations"

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Kawai, Shingo. "Isomonodromic deformation of Fuchsian projective connections on elliptic curves." Nagoya Mathematical Journal 171 (2003): 127–61. http://dx.doi.org/10.1017/s002776300002554x.

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AbstractWe consider isomonodromic deformations of second-order Fuchsian differential equations on elliptic curves. The isomonodromic deformations are described as a completely integrable Hamiltonian system.
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Korotkin, D., and H. Samtleben. "On the Quantization of Isomonodromic Deformations on the Torus." International Journal of Modern Physics A 12, no. 11 (1997): 2013–29. http://dx.doi.org/10.1142/s0217751x97001274.

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The quantization of isomonodromic deformation of a meromorphic connection on the torus is shown to lead directly to the Knizhnik–Zamolodchikov–Bernard equations in the same way as the problem on the sphere leads to the system of Knizhnik–Zamolodchikov equations. The Poisson bracket required for a Hamiltonian formulation of isomonodromic deformations is naturally induced by the Poisson structure of Chern–Simons theory in a holomorphic gauge fixing. This turns out to be the origin of the appearance of twisted quantities on the torus.
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Doran, Charles F. "Algebraic and Geometric Isomonodromic Deformations." Journal of Differential Geometry 59, no. 1 (2001): 33–85. http://dx.doi.org/10.4310/jdg/1090349280.

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Boalch, Philip. "Symplectic Manifolds and Isomonodromic Deformations." Advances in Mathematics 163, no. 2 (2001): 137–205. http://dx.doi.org/10.1006/aima.2001.1998.

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Babich, Mikhail V. "Isomonodromic Deformations and Painlevé Equations." Constructive Approximation 41, no. 3 (2015): 335–56. http://dx.doi.org/10.1007/s00365-015-9286-2.

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Cotti, Giordano, and Davide Guzzetti. "Results on the extension of isomonodromy deformations to the case of a resonant irregular singularity." Random Matrices: Theory and Applications 07, no. 04 (2018): 1840003. http://dx.doi.org/10.1142/s2010326318400038.

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We explain some results of [G. Cotti, B. A. Dubrovin and D. Guzzetti, Isomonodromy deformations at an irregular singularity with coalescing eigenvalues, preprint (2017); arXiv:1706.04808 .], discussed in our talk [G. Cotti, Monodromy of semisimple Frobenius coalescent structures, in Int. Workshop Asymptotic and Computational Aspects of Complex Differential Equations, CRM, Pisa, February 13–17, (2017).] in Pisa, February 2017. Consider an [Formula: see text] linear system of ODEs with an irregular singularity of Poincaré rank 1 at [Formula: see text] and Fuchsian singularity at [Formula: see te
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Yamakawa, Daisuke. "Fourier-Laplace Transform and Isomonodromic Deformations." Funkcialaj Ekvacioj 59, no. 3 (2016): 315–49. http://dx.doi.org/10.1619/fesi.59.315.

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TAKASAKI, KANEHISA, and TOSHIO NAKATSU. "ISOMONODROMIC DEFORMATIONS AND SUPERSYMMETRIC GAUGE THEORIES." International Journal of Modern Physics A 11, no. 31 (1996): 5505–18. http://dx.doi.org/10.1142/s0217751x96002522.

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Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those various features of integrability. The Seiberg-Witten solution itself can be interpreted as a WKB limit of this isomonodromy problem. The origin of underlying Whitham dynamics (adiabatic deformation of an isospectral problem) too can be similarly explained by a more refined asymptotic method (multiscale analysis). The case of N = 2 SU (s) supersymmetric Yang
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Korotkin, D., N. Manojlović, and H. Samtleben. "Schlesinger transformations for elliptic isomonodromic deformations." Journal of Mathematical Physics 41, no. 5 (2000): 3125–41. http://dx.doi.org/10.1063/1.533296.

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Sanguinetti, G., and N. M. J. Woodhouse. "The geometry of dual isomonodromic deformations." Journal of Geometry and Physics 52, no. 1 (2004): 44–56. http://dx.doi.org/10.1016/j.geomphys.2004.01.005.

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Dissertations / Theses on the topic "Isomonodromic deformations"

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Boalch, Philip Paul. "Symplectic geometry and isomonodromic deformations." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301848.

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Díaz, Arboleda Juan Sebastián. "Isomonodromic deformations through differential Galois theory." Thesis, Rennes 1, 2019. http://www.theses.fr/2019REN1S089.

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Le texte commence par une brève description de théorie différentielle de Galois dans une perspective géométrique. Ensuite, la théorie paramétrée de Galois est développée au moyen d’une prolongation des connexions partielles avec les fibrés de jets. La relation entre les groupes de Galois différentiels a paramètres et les déformations isomonodromiques est développée comme une application du théorème de Kiso-Cassidy. Il s’ensuit le calcul des groupes de Galois a paramètres de l’équation générale fuchsienne et de l’équation hypergéométrique de Gauss. Enfin, certaines applications non linéaires so
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3

Horrobin, Calum. "Stokes' Phenomenon arising from the confluence of two simple poles." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/28357.

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We study certain confluences of equations with two Fuchsian singularities which produce an irregular singularity of Poincaré rank one. We demonstrate a method to understand how to pass from solutions with power-like behavior which are analytic in neighbourhoods to solutions with exponential behavior which are analytic in sectors and have divergent asymptotic behavior. We explicitly calculate the Stokes' matrices of the confluent system in terms of the monodromy data, specifically the connection matrices, of the original system around the merging singularities. The confluence of Gauss' hyperge
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Boalch, Philip. "Geometry of moduli spaces of meromorphic connections on curves, Stokes data, wild nonabelian Hodge theory, hyperkahler manifolds, isomonodromic deformations, Painleve equations, and relations to Lie theory." Habilitation à diriger des recherches, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00768643.

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Girand, Arnaud. "Équations d'isomonodromie, solutions algébriques et dynamique." Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S042/document.

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Une déformation isomonodromique d'une sphère épointée est une famille de connexions logarithmiques plates sur cette dernière ayant toutes, à conjugaison globale près, la même représentation de monodromie. Ces objets sont paramétrés par les solutions d'une certaine famille d'équations aux dérivées partielles, les systèmes de Garnier, qui sont équivalents dans le cas de la sphère à quatre trous aux équations de Painlevé VI. L'objet des travaux présentés ici est de construire de nouvelles solutions algébriques des ces systèmes dans le cas de la sphère à cinq trous. Dans une première partie, nous
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Davey, Robert Michael. "SMJ analysis of monodromy fields." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184357.

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The connection discovered by M. Sato, T. Miwa and M. Jimbo (SMJ) between the monodromy-preserving deformation theory of the two-dimensional Euclidean Dirac operator and quantum fields is rigorously established for the case of nonreal S¹ monodromy parameters. This connection involves the expression of the associated n-point functions in terms of solutions to deformation equations which arise as necessary conditions for the monodromy exhibited by a class of multivalued solutions of the Euclidean Dirac equation to be preserved under perturbations of branch points. Our approach utilizes recent res
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Milne, Alice Elizabeth. "The Painleve equations : Bäcklund transformations, exact solutions and the isomonodromy deformation method". Thesis, University of Exeter, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.261748.

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Books on the topic "Isomonodromic deformations"

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Isomonodromic deformations and Frobenius manifolds: An introduction. Springer, 2008.

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2

ŁU, Novokshenov V. I., ed. The isomonodromic deformation method in the theory of Painleve equations. Springer-Verlag, 1986.

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Yu, Novokshenov Victor, ed. The isomonodromic deformation method in the theory of Painlevé equations. Springer-Verlag, 1986.

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Its, Alexander R., and Victor Yu Novokshenov. The Isomonodromic Deformation Method in the Theory of Painlevé Equations. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076661.

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Sabbah, Claude. De formations isomonodromiques et varie te s de Frobenius. EDP Sciences, 2002.

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6

Dzhamay, Anton, Ken'ichi Maruno, and Christopher M. Ormerod. Algebraic and analytic aspects of integrable systems and painleve equations: AMS special session on algebraic and analytic aspects of integrable systems and painleve equations : January 18, 2014, Baltimore, MD. American Mathematical Society, 2015.

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Isomonodromic Deformations and Frobenius Manifolds. Springer London, 2008. http://dx.doi.org/10.1007/978-1-84800-054-4.

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Takashi, Aoki, and Kyōto Daigaku. Sūri Kaiseki Kenkyūjo., eds. Virtual turning points and isomonodromic deformations. Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2006.

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9

(Editor), John P. Harnad, and Alexander R. Its (Editor), eds. Isomonodromic Deformations and Applications in Physics. American Mathematical Society, 2002.

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Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices Ams Special Session Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices January 67 2012 Boston Ma. American Mathematical Society, 2013.

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Book chapters on the topic "Isomonodromic deformations"

1

Korotkin, D. "Isomonodromic deformations and Hurwitz spaces." In CRM Proceedings and Lecture Notes. American Mathematical Society, 2002. http://dx.doi.org/10.1090/crmp/031/04.

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Olshanetsky, M. "𝑊-geometry and isomonodromic deformations." In CRM Proceedings and Lecture Notes. American Mathematical Society, 2002. http://dx.doi.org/10.1090/crmp/031/06.

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Harnad, John. "Quantum isomonodromic deformations and the Knizhnik-Zamolodchikov equations." In CRM Proceedings and Lecture Notes. American Mathematical Society, 1996. http://dx.doi.org/10.1090/crmp/009/15.

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Harnad, J. "Bispectral operators of rank 1 and dual isomonodromic deformations." In CRM Proceedings and Lecture Notes. American Mathematical Society, 1997. http://dx.doi.org/10.1090/crmp/011/07.

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Doran, Charles. "Algebro-geometric isomonodromic deformations linking Hauptmoduls: Variation of the mirror map." In CRM Proceedings and Lecture Notes. American Mathematical Society, 2001. http://dx.doi.org/10.1090/crmp/030/03.

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Mazzocco, Marta. "Painlevé sixth equation as isomonodromic deformations equation of an irregular system." In The Kowalevski Property. American Mathematical Society, 2002. http://dx.doi.org/10.1090/crmp/032/12.

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Its, Alexander R., and Victor Yu Novokshenov. "Isomonodromic deformations of systems of linear ordinary differential equations with rational coefficients." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076664.

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Korotkin, D. "Isomonodromic deformations in genus zero and one: Algebro-geometric solutions and Schlesinger transformations." In CRM Proceedings and Lecture Notes. American Mathematical Society, 2000. http://dx.doi.org/10.1090/crmp/026/05.

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Its, Alexander R., and Victor Yu Novokshenov. "Isomonodromic deformations of systems (1.9) and (1.26) and painlevé equations of II and III types." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076665.

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Mahoux, Gilbert. "Introduction to the Theory of Isomonodromic Deformations of Linear Ordinary Differential Equations with Rational Coefficients." In The Painlevé Property. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1532-5_2.

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Conference papers on the topic "Isomonodromic deformations"

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WU, DERCHYI. "ON ISOMONODROMY DEFORMATIONS FOR THE ZS-AKNS FLOWS." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704467_0019.

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