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Polynomial bounds for the oscillation of solutions of Fuchsian systems

Gal Binyamini, Sergei Yakovenko (2009)

Annales de l’institut Fourier

We study the problem of placing effective upper bounds for the number of zeroes of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of Fuchsian systems of a given dimension n having m singular points. As a function of n , m , this bound turns out to be double exponential in the precise sense explained in the paper.As a corollary, we obtain a solution of the so-called restricted infinitesimal...

Pseudo-abelian integrals on slow-fast Darboux systems

Marcin Bobieński, Pavao Mardešić, Dmitry Novikov (2013)

Annales de l’institut Fourier

We study pseudo-abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number of their zeros.

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