DOI: https://doi.org/10.18524/1810-4215.2017.30.114229

CORRELATION OF THE NUMBER OF IMAGES OF AN N-POINT GRAVITATIONAL LENS AND THE NUMBER OF SOLUTIONS OF ITS SYSTEM

A. T. Kotvytskiy, S. D. Bronza, V. Yu. Shablenko

Анотація


In this paper, we study the correlation between the number of solutions of a system of lens equations and the number of source images that a gravitational lens has. We defined the concept of an image in a gravitational lens. To find the set of solutions of a system of lens equations, we applied methods of algebraic geometry.


Ключові слова


Lens; gravitational lenses; images; solutions; Algebraic geometry; resultant; Bezout theorem

Повний текст:

PDF (English)

Посилання


Arzhancev I.V.: 2003, Basisy Grebnera i systemy algebraicheskikh uravneniy [in Russian]. Letnyaya shkola, Sovremennaya matematika. Moskow, P. 68.

Bliokh P.V. & Minakov A.A.: 1989, Gravitational Lenses [in Russian], Naukova Dumka, Kiev.

Bronza S.D.: 2016, Zbirnik naukovih prats, Kharkiv, UkrURT, 68 [in Russian].

Bronza S.D., Kotvytskiy A.T.: 2017, The Journal of Kharkiv National University, ser. Physics, 26(1120, 6.

Kalinina E.A., Uteshev A.Yu.: 2002, Teoriaisklyucheniya, SPBU, Saint Petersburg, 72.

Kotvytskiy A.T., Bronza S.D.: 2016, Odessa Astron. Publ., 29, 31.

Kotvytskiy A.T., Bronza S.D., Vovk S.R.: 2016, The Journal of Kharkiv National University, ser. Physics, 24(1119), 55.

Kotvytskiy A.T., Bronza S.D., Nerushenko K.Yu., Shablenko V.Yu.: 2017, Zbirnik naukhovih prats VI Mizhregionalnoyi naukovo-praktichnoyi konferencii ”Astronomiya i syogodennya”, Vinnitsya, [in Ukrainian], 198.

Lang S.: Algebra. Columbia University. New York, 1965.

Reid Milies A.: 1988, Undergraduate Algebraic Geometry, 151.

Schneider P., Ehlers J., Falco E.E.: 1999, Gravitational lenses, 560.

Van Der Waerden B.L.: 1971, Algebra I, II, P. 456.

Walker R.J.: 1950, Algebraic curves, P. 236.

Zakharov A.F.: 1997, Gravitacionnye linzy i mikrolinzy, 328.




Copyright (c) 2017 Odessa Astronomical Publications

Creative Commons License
Ця робота ліцензована Creative Commons Attribution-NonCommercial 4.0 International License.