On uniform symmetrization of analytic matrix functions
J. Kisyński (1972)
Studia Mathematica
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J. Kisyński (1972)
Studia Mathematica
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Tatsuo Nishitani, Sergio Spagnolo (2001)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Hans-Joachim Zwiesler (1997)
Publicacions Matemàtiques
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In this article we investigate the question [of] how meromorphic differential equations can be simplified by meromorphic equivalence. In the case of equations of block size 1, which generalizes the case of distinct eigenvalues, we identify a class of equations which are simplest possible in the sense that they carry the smallest number of parameters whithin their equivalence classes. We also discuss conditions under which individual equations can be simplified. Particular attention is...
Peter Breitenlohner, Dieter Maison (1987)
Annales de l'I.H.P. Physique théorique
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Pavel M. Bleher, Alexander Its (2005)
Annales de l’institut Fourier
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We prove a number of results concerning the large asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics...
Amadeu Delshams, Arnau Mir (1997)
Publicacions Matemàtiques
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Psi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is proved that quadratic systems with psi-series that are not Laurent series do not have an algebraic first integral. Besides, a criterion about non-existence...