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It is shown that the lens equation for a binary gravitational lens being a set of two coupled real fifth-order algebraic equations (equivalent to a single complex equation of the same order) can be reduced to a single real fifth-order…

The Euclidean algorithm in algebra is applied to a class of gravitational lenses for which the lens equation consists of any set of coupled polynomial equations in the image position. In general, this algorithm allows us to reduce an…

The gravitational lens equation for the tilted Plummer family of models can be reduced to a one-dimensional non-linear equation. For certain values of the slope of the radial profile it can be reduced to a polynomial form. Both forms are…

We present explicit expressions for the lens equation for a cored isothermal ellipsoidal gravitational lens as a single real sixth-order algebraic equation in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar ones.…

Despite its mathematical complexity, the multiple gravitational lens can be studied in detail in every situation where a perturbative approach is possible. In this paper, we examine the caustics of a system with a lens very far from the…

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…

We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image…

Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first…

The strange morphology of the six-component gravitational lens PMN J0134-0931 has resisted explanation. We present the first successful quantitative models for the system, based on the idea that there are two lens galaxies and two…

Generalizing a result for the binary lens, similar alternative expressions are also given for the Jacobian determinant for a gravitational lens consisting of an arbitrary number of discrete lensing centres, with arbitrary masses and…

When the gravitational lensing potential can be approximated by that of circularly symmetric system affected by weak perturbations, it is found that the shape of the resulting (tangential) caustics is entirely specified by the local…

The cusps of the caustics of any gravitational lens model can be classified into positive and negative ones. This distinction lies on the parity of the images involved in the creation/destruction of pairs occurring when a source crosses a…

It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily…

It is shown which properties of a strong gravitational lens can in principle be recovered from observations of multiple extended images when no assumptions are made about the deflector or sources. The mapping between individual multiple…

We study analytically a gravitational lens due to a deformed star, which is modeled by using a monopole and a quadrupole moment. Positions of the images are discussed for a source on the principal axis. We present explicit expressions for…

We present the first detailed computations of wave optics effects in the gravitational lensing of binary systems. The field is conceptually rich, combining the caustic singularities produced in classical gravitational lensing with quantum…

We investigated the effects of gravitational lensing for a system in which a lens is a point mass and a homogeneous disc with a central hole. In such system there is a variety of cases resulting in formation of one, two and three Einstein…

The study of light lensed by cosmic matter has yielded much information about astrophysical questions. Observations are explained using geometrical optics following a ray-based description of light. After deflection the lensed light…

One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…

The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…