Displaying similar documents to “Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves”

Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.

Yulin Zhao, Zhifen Zhang (2000)

Publicacions Matemàtiques

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It is proved in this paper that the maximum number of limit cycles of system ⎧ dx/dt = y ⎨ ⎩ dy/dt = kx - (k + 1)x2 + x3 + ε(α + βx + γx2)y is equal to two in the finite plane, where k > (11 + √33) / 4 , 0 < |ε| << 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.

Analytic continuation of fundamental solutions to differential equations with constant coefficients

Christer O. Kiselman (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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If P is a polynomial in R n such that 1 / P integrable, then the inverse Fourier transform of 1 / P is a fundamental solution E P to the differential operator P ( D ) . The purpose of the article is to study the dependence of this fundamental solution on the polynomial P . For n = 1 it is shown that E P can be analytically continued to a Riemann space over the set of all polynomials of the same degree as P . The singularities of this extension are studied.