نتایج جستجو برای: zeros of abelian integrals
تعداد نتایج: 21170995 فیلتر نتایج به سال:
We study the analogue of the infinitesimal 16th Hilbert problem in dimension zero. Lower and upper bounds for the number of the zeros of the corresponding Abelian integrals (which are algebraic functions) are found. We study the relation between the vanishing of an Abelian integral I(t) defined over Q and its arithmetic properties. Finally, we give necessary and sufficient conditions for an Abe...
We derive an explicit system of Picard–Fuchs differential equations satisfied by Abelian integrals of monomial forms and majorize its coefficients. A peculiar feature of this construction is that the system admitting such explicit majorants, appears only in dimension approximately two times greater than the standard Picard–Fuchs system. The result is used to obtain a partial solution to the tan...
These notes form an extended version of a minicourse delivered in Université de Montréal (June 2002) within the framework of a NATO workshop “Normal Forms, Bifurcations and Finiteness Problems in Differential Equations”. The focus is on Poincaré–Dulac theory of “Fuchsian” (logarithmic) singularities of integrable systems, with applications to problems on zeros of Abelian integrals in view.
These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this study was its potential application to the tangential Hilbert 16th problem on zeros of complete Abelian integrals. The exposition consists mostly of examples ill...
These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this study was its potential application to the tangential Hilbert 16th problem on zeros of complete Abelian integrals. The exposition consists mostly of examples ill...
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