Displaying similar documents to “Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group.”

Simple exponential estimate for the number of real zeros of complete abelian integrals

Dmitri Novikov, Sergei Yakovenko (1995)

Annales de l'institut Fourier

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We show that for a generic polynomial H = H ( x , y ) and an arbitrary differential 1-form ω = P ( x , y ) d x + Q ( x , y ) d y with polynomial coefficients of degree ≤ d , the number of ovals of the foliation H = const , which yield the zero value of the complete Abelian integral I ( t ) = ∮ H = t ω , grows at most as exp O H ( d ) as d → ∞ , where O H ( d ) depends only on H . The main result of the paper is derived from the following more general theorem on bounds for isolated zeros occurring in polynomial envelopes of linear differential equations. Let f 1 ( t ) , ⋯ , f n ( t ) , t ∈ K ⋐ ℝ , be a fundamental system of...

Pseudo-abelian integrals on slow-fast Darboux systems

Marcin Bobieński, Pavao Mardešić, Dmitry Novikov (2013)

Annales de l’institut Fourier

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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.