Yves Colin de Verdière (2003)
Annales de l’institut Fourier
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We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.
Hironobu Kimura (1993)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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H. P. Künzle (1969)
Annales de l'I.H.P. Physique théorique
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Hector Giacomini, Malick Ndiaye (1996)
Publicacions Matemàtiques
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In this paper, we consider polynomial systems of the form x' = y + P(x, y), y' = -x + Q(x, y), where P and Q are polynomials of degree n wihout linear part. For the case n = 3, we have found new sufficient conditions for a center at the origin, by proposing a first integral linear in certain coefficient of the system. The resulting first integral is in the general case of Darboux type. By induction, we have been able to generalize these results for polynomial...
Emil Horozov (2005)
Annales de l’institut Fourier
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We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.
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...