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Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: In this paper, the number of limit cycles which can bifurcate from the periodic orbits of the two centers was studied using the averaging theory of first, second and third orders.
9 citations
TL;DR: In this paper, the authors studied the global behaviour of the normal function associated with van Geemen's family of lines on the mirror quintic and derived the series expansions around large complex structure, conifold, and around the open string discriminant.
Abstract: The global behaviour of the normal function associated with van Geemen's family of lines on the mirror quintic is studied. Based on the associated inhomogeneous Picard{Fuchs equation, the series expansions around large complex structure, conifold, and around the open string discriminant are obtained. The monodromies are explicitly calculated from this data and checked to be integral. The limiting value of the normal function at large complex structure is an irrational number expressible in terms of the di-logarithm.
9 citations
TL;DR: The first exact result on open string mirror symmetry for a compact Calabi-Yau manifold was given in this article, where the tension of the domainwall between the two vacua on the brane satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic.
Abstract: Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open Gromov-Witten invariants, satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space. We reproduce the first few instanton numbers by a localization computation directly in the A-model, and check Ooguri-Vafa integrality. This is the first exact result on open string mirror symmetry for a compact Calabi-Yau manifold.
9 citations
TL;DR: In this paper, the authors present an explicit algorithm for solving a general quintic, which employs one 3-dimensional iteration, in contrast to the Doyle-McMullen procedure, which involves three 1-dimensional iterations, and culminates with a rational map in degree six.
Abstract: The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S5 Induced by its five-dimensional linear permutation representation is a three-dimensional projective action. A mapping of complex projective 3-space with this S5 symmetry can provide the requisite symmetry-breaking tool. The article describes some of the S5 geometry in CP3 as well as several maps with particu larly elegant geometric and dynamical properties. Using a rational map in degree six, it culminates with an explicit algorithm for solving a general quintic. In contrast to the Doyle-McMullen procedure, which involves three 1-dimensional iterations, the present solution employs one 3-dimensional iteration.
9 citations
TL;DR: This work applies point canonical transformations to solve some classes of nonautonomous, nonlinear Schrödinger equations, namely, those which possess specific cubic and quintic (time- and space-dependent) nonlinearities.
Abstract: In this work we apply point canonical transformations to solve some classes of nonautonomous, nonlinear Schr\"odinger equations, namely, those which possess specific cubic and quintic (time- and space-dependent) nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wave function and recover a time- and space-independent nonlinear equation which can be solved explicitly. The method applied here allows us to find wide localized (in space) soliton solutions to the nonautonomous, nonlinear Schr\"odinger equation. We also generalize the external potential which traps the system and the terms of the nonlinearities.
9 citations