Results 171 to 180 of about 121,182 (204)

The monotonicity of ratios of some Abelian integrals

Bulletin des Sciences Mathématiques, 2021
In this paper, the authors study the monotonicity of the ratio of the abelian integrals \[\frac{\oint_{\gamma_i(h)} xy\ \mathrm{d}x}{\oint_{\gamma_i(h)} y\ \mathrm{d}x},\] in an interval, where \(i=1,2\), and \(\gamma_i(h)\) is a compact component of some hyperelliptic curves with genus 2 as \(h\in\gamma_i(h)\).
Sun, Xianbo, Wang, Na, Yu, Pei
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Linear Estimate for the Number of Zeros of Abelian Integrals [PDF]

Qualitative Theory of Dynamical Systems, 2016
We prove a linear in $\degω$ upper bound on the number of real zeros of the Abelian integral $I(t)=\int_{δ(t)}ω$, where $δ(t)\subset\R^2$ is the real oval $x^2y(1-x-y)=t$ and $ω$ is a one-form with polynomial coefficients.
Dmitry Novikov, Sergey Malev
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Abelian Integrals and Limit Cycles

Qualitative Theory of Dynamical Systems, 2011
In this survey paper, the author discusses the interconnection of the problem of estimating the number of limit cycles of planar polynomial systems (Hilbert's 16th problem) and the problem of estimating the number of isolated zeros of certain abelian integrals. In the first part of the paper, some basic concepts and methods are introduced.
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Non-Abelian prolongations and complete integrability

Physica D: Nonlinear Phenomena, 1981
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Leo, M., Leo, R. A., Martina, L., Pirani, F. A. E., Soliani, G.   +4 more
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Abelian and non-Abelian bosonization in the path-integral framework

Physical Review D, 1985
Abelian and non-Abelian bosonization of two-dimensional models is discussed within the path-integral framework. Concerning the Abelian case, the equivalence between the massive Thirring and the sine-Gordon models is rederived in a very simple way by making a chiral change in the fermionic path-integral variables.
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Some Identities for Abelian Integrals

American Journal of Mathematics, 1986
The author studies subvarieties in the Jacobi variety of a compact Riemann surface at which certain matrices of second-order theta-functions have exceptionally low ranks. The obtained linear relations between second-order theta-functions involve Abelian integrals and present themselves a natural generalization of Fay's trisecant formula.
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Algebraic independence of the periods of abelian integrals

Mathematical Notes, 1996
The author considers an irreducible algebraic curve of genus \(g\leq 1\) over the field of algebraic numbers \(\mathbb{A}\). On the Riemann surface of the curve there exist \(2g\) Abelian differentials of the second kind \(\phi_1,\dots, \phi_{2g}\) over \(\mathbb{A}\) and \(2g\) cycles \(\gamma_1,\dots, \gamma_{2g}\) such that the matrix \(\Omega ...
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Inversion of abelian integrals

Archiv der Mathematik, 1988
Given a projective non-singular curve of genus g and an integer \(k\geq 2g- 1\), the natural map from the k-symmetric product of the curve to the jacobian is a projective bundle. The pull-back of this bundle to the universal cover of the jacobian is trivial and it should be possible to describe the bundle by means of multiplicative factors. This is the
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Elliptic and Abelian Integrals

2017
With the innovations of calculus, it was discovered that standard trigonometric functions could be formulated as integrals of algebraic function of degree two. Euler and others generalized these to elliptic integrals, integrals of algebraic functions of degree three and four, and Abel generalized these, in turn, to integrals of algebraic functions of ...
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Abelian Integrals Attached to Algebraic Varieties

The Mathematical Gazette, 1933
The purpose of this article is to describe briefly some investigations of the properties of certain integrals associated with the Riemannian manifold of an algebraic variety, which, besides having an interest of their own, appear to be a fruitful source of new properties of the more classical Abelian integrals usually considered in connection with ...
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